LMFDB - Embedded newform 260.2.o.a.27.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(27,260)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("260.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.o (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.34
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.34

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32335 + 0.498731i) q^{2} +(1.08931 + 1.08931i) q^{3} +(1.50254 + 1.32000i) q^{4} +(-0.398291 - 2.20031i) q^{5} +(0.898273 + 1.98482i) q^{6} +(-0.555275 + 0.555275i) q^{7} +(1.33007 + 2.49618i) q^{8} -0.626800i q^{9} +O(q^{10})$	\(q+(1.32335 + 0.498731i) q^{2} +(1.08931 + 1.08931i) q^{3} +(1.50254 + 1.32000i) q^{4} +(-0.398291 - 2.20031i) q^{5} +(0.898273 + 1.98482i) q^{6} +(-0.555275 + 0.555275i) q^{7} +(1.33007 + 2.49618i) q^{8} -0.626800i q^{9} +(0.570281 - 3.11043i) q^{10} +2.61255i q^{11} +(0.198844 + 3.07462i) q^{12} +(0.707107 - 0.707107i) q^{13} +(-1.01176 + 0.457894i) q^{14} +(1.96296 - 2.83069i) q^{15} +(0.515226 + 3.96668i) q^{16} +(-2.63640 - 2.63640i) q^{17} +(0.312604 - 0.829478i) q^{18} -5.53821 q^{19} +(2.30595 - 3.83179i) q^{20} -1.20974 q^{21} +(-1.30296 + 3.45733i) q^{22} +(-0.817097 - 0.817097i) q^{23} +(-1.27026 + 4.16798i) q^{24} +(-4.68273 + 1.75273i) q^{25} +(1.28841 - 0.583097i) q^{26} +(3.95072 - 3.95072i) q^{27} +(-1.56728 + 0.101360i) q^{28} -1.74233i q^{29} +(4.00944 - 2.76701i) q^{30} -1.39981i q^{31} +(-1.29648 + 5.50628i) q^{32} +(-2.84588 + 2.84588i) q^{33} +(-2.17404 - 4.80375i) q^{34} +(1.44294 + 1.00062i) q^{35} +(0.827373 - 0.941789i) q^{36} +(-0.838546 - 0.838546i) q^{37} +(-7.32902 - 2.76208i) q^{38} +1.54052 q^{39} +(4.96262 - 3.92076i) q^{40} +0.268446 q^{41} +(-1.60091 - 0.603332i) q^{42} +(3.82216 + 3.82216i) q^{43} +(-3.44855 + 3.92545i) q^{44} +(-1.37915 + 0.249649i) q^{45} +(-0.673798 - 1.48882i) q^{46} +(8.05542 - 8.05542i) q^{47} +(-3.75971 + 4.88219i) q^{48} +6.38334i q^{49} +(-7.07105 - 0.0159388i) q^{50} -5.74373i q^{51} +(1.99583 - 0.129076i) q^{52} +(6.61129 - 6.61129i) q^{53} +(7.19854 - 3.25786i) q^{54} +(5.74842 - 1.04056i) q^{55} +(-2.12462 - 0.647516i) q^{56} +(-6.03284 - 6.03284i) q^{57} +(0.868951 - 2.30571i) q^{58} -12.1770 q^{59} +(6.68591 - 1.66211i) q^{60} +9.92235 q^{61} +(0.698126 - 1.85244i) q^{62} +(0.348046 + 0.348046i) q^{63} +(-4.46185 + 6.64017i) q^{64} +(-1.83749 - 1.27422i) q^{65} +(-5.18544 + 2.34678i) q^{66} +(-4.22053 + 4.22053i) q^{67} +(-0.481251 - 7.44133i) q^{68} -1.78015i q^{69} +(1.41048 + 2.04381i) q^{70} +11.5670i q^{71} +(1.56461 - 0.833685i) q^{72} +(-7.67772 + 7.67772i) q^{73} +(-0.691485 - 1.52790i) q^{74} +(-7.01022 - 3.19168i) q^{75} +(-8.32136 - 7.31041i) q^{76} +(-1.45068 - 1.45068i) q^{77} +(2.03865 + 0.768304i) q^{78} -6.13415 q^{79} +(8.52271 - 2.71355i) q^{80} +6.72672 q^{81} +(0.355249 + 0.133882i) q^{82} +(2.27045 + 2.27045i) q^{83} +(-1.81767 - 1.59685i) q^{84} +(-4.75085 + 6.85096i) q^{85} +(3.15185 + 6.96431i) q^{86} +(1.89794 - 1.89794i) q^{87} +(-6.52140 + 3.47486i) q^{88} +5.29932i q^{89} +(-1.94962 - 0.357452i) q^{90} +0.785278i q^{91} +(-0.149153 - 2.30628i) q^{92} +(1.52482 - 1.52482i) q^{93} +(14.6777 - 6.64270i) q^{94} +(2.20582 + 12.1858i) q^{95} +(-7.41033 + 4.58579i) q^{96} +(-3.44319 - 3.44319i) q^{97} +(-3.18357 + 8.44742i) q^{98} +1.63755 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) $ 72 * q - 8 * q^6 - 12 * q^8	$ 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) $ 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.32335	+	0.498731i	0.935753	+	0.352656i
$2$	1.32335	+	0.498731i	0.935753	+	0.352656i
$3$	1.08931	+	1.08931i	0.628914	+	0.628914i	0.947795	−	0.318880i	$-0.103307\pi$
$3$	1.08931	+	1.08931i	0.628914	+	0.628914i	−0.318880	+	0.947795i	$0.603307\pi$
$4$	1.50254	+	1.32000i	0.751268	+	0.659998i
$5$	−0.398291	−	2.20031i	−0.178121	−	0.984009i
$5$	−0.398291	−	2.20031i	−0.178121	−	0.984009i
$6$	0.898273	+	1.98482i	0.366718	+	0.810299i
$7$	−0.555275	+	0.555275i	−0.209874	+	0.209874i	−0.804214	−	0.594340i	$-0.797413\pi$
$7$	−0.555275	+	0.555275i	−0.209874	+	0.209874i	0.594340	+	0.804214i	$0.297413\pi$
$8$	1.33007	+	2.49618i	0.470249	+	0.882534i
$9$		−	0.626800i		−	0.208933i
$10$	0.570281	−	3.11043i	0.180339	−	0.983605i
$11$			2.61255i			0.787713i	0.919172	+	0.393857i	$0.128859\pi$
$11$			2.61255i			0.787713i	−0.919172	+	0.393857i	$0.871141\pi$
$12$	0.198844	+	3.07462i	0.0574012	+	0.887565i
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$14$	−1.01176	+	0.457894i	−0.270404	+	0.122377i
$15$	1.96296	−	2.83069i	0.506834	−	0.730880i
$16$	0.515226	+	3.96668i	0.128807	+	0.991670i
$17$	−2.63640	−	2.63640i	−0.639422	−	0.639422i	0.310991	−	0.950413i	$-0.399339\pi$
$17$	−2.63640	−	2.63640i	−0.639422	−	0.639422i	−0.950413	+	0.310991i	$0.899339\pi$
$18$	0.312604	−	0.829478i	0.0736815	−	0.195510i
$19$	−5.53821			−1.27055			−0.635276	−	0.772285i	$-0.719114\pi$
$19$	−5.53821			−1.27055			−0.635276	+	0.772285i	$0.719114\pi$
$20$	2.30595	−	3.83179i	0.515626	−	0.856813i
$21$	−1.20974			−0.263986
$22$	−1.30296	+	3.45733i	−0.277792	+	0.737105i
$23$	−0.817097	−	0.817097i	−0.170376	−	0.170376i	0.616768	−	0.787145i	$-0.288442\pi$
$23$	−0.817097	−	0.817097i	−0.170376	−	0.170376i	−0.787145	+	0.616768i	$0.788442\pi$
$24$	−1.27026	+	4.16798i	−0.259292	+	0.850785i
$25$	−4.68273	+	1.75273i	−0.936546	+	0.350546i
$26$	1.28841	−	0.583097i	0.252678	−	0.114355i
$27$	3.95072	−	3.95072i	0.760316	−	0.760316i
$28$	−1.56728	+	0.101360i	−0.296188	+	0.0191553i
$29$		−	1.74233i		−	0.323542i	−0.986828	−	0.161771i	$-0.948279\pi$
$29$		−	1.74233i		−	0.323542i	0.986828	−	0.161771i	$-0.0517205\pi$
$30$	4.00944	−	2.76701i	0.732021	−	0.505185i
$31$		−	1.39981i		−	0.251412i	−0.992068	−	0.125706i	$-0.959880\pi$
$31$		−	1.39981i		−	0.251412i	0.992068	−	0.125706i	$-0.0401197\pi$
$32$	−1.29648	+	5.50628i	−0.229187	+	0.973382i
$33$	−2.84588	+	2.84588i	−0.495404	+	0.495404i
$34$	−2.17404	−	4.80375i	−0.372845	−	0.823837i
$35$	1.44294	+	1.00062i	0.243901	+	0.169135i
$36$	0.827373	−	0.941789i	0.137895	−	0.156965i
$37$	−0.838546	−	0.838546i	−0.137856	−	0.137856i	0.634811	−	0.772667i	$-0.281078\pi$
$37$	−0.838546	−	0.838546i	−0.137856	−	0.137856i	−0.772667	+	0.634811i	$0.781078\pi$
$38$	−7.32902	−	2.76208i	−1.18892	−	0.448068i
$39$	1.54052			0.246681
$40$	4.96262	−	3.92076i	0.784659	−	0.619927i
$41$	0.268446			0.0419242			0.0209621	−	0.999780i	$-0.493327\pi$
$41$	0.268446			0.0419242			0.0209621	+	0.999780i	$0.493327\pi$
$42$	−1.60091	−	0.603332i	−0.247026	−	0.0930962i
$43$	3.82216	+	3.82216i	0.582874	+	0.582874i	0.935692	−	0.352818i	$-0.114776\pi$
$43$	3.82216	+	3.82216i	0.582874	+	0.582874i	−0.352818	+	0.935692i	$0.614776\pi$
$44$	−3.44855	+	3.92545i	−0.519889	+	0.591784i
$45$	−1.37915	+	0.249649i	−0.205592	+	0.0372154i
$46$	−0.673798	−	1.48882i	−0.0993460	−	0.219515i
$47$	8.05542	−	8.05542i	1.17500	−	1.17500i	0.194004	−	0.981001i	$-0.437853\pi$
$47$	8.05542	−	8.05542i	1.17500	−	1.17500i	0.981001	−	0.194004i	$-0.0621473\pi$
$48$	−3.75971	+	4.88219i	−0.542667	+	0.704684i
$49$			6.38334i			0.911905i
$50$	−7.07105	−	0.0159388i	−0.999997	−	0.00225408i
$51$		−	5.74373i		−	0.804284i
$52$	1.99583	−	0.129076i	0.276772	−	0.0178996i
$53$	6.61129	−	6.61129i	0.908131	−	0.908131i	−0.0879906	−	0.996121i	$-0.528045\pi$
$53$	6.61129	−	6.61129i	0.908131	−	0.908131i	0.996121	+	0.0879906i	$0.0280445\pi$
$54$	7.19854	−	3.25786i	0.979597	−	0.443338i
$55$	5.74842	−	1.04056i	0.775117	−	0.140308i
$56$	−2.12462	−	0.647516i	−0.283914	−	0.0865280i
$57$	−6.03284	−	6.03284i	−0.799069	−	0.799069i
$58$	0.868951	−	2.30571i	0.114099	−	0.302755i
$59$	−12.1770			−1.58531			−0.792656	−	0.609669i	$-0.791302\pi$
$59$	−12.1770			−1.58531			−0.792656	+	0.609669i	$0.791302\pi$
$60$	6.68591	−	1.66211i	0.863147	−	0.214577i
$61$	9.92235			1.27043			0.635213	−	0.772337i	$-0.280912\pi$
$61$	9.92235			1.27043			0.635213	+	0.772337i	$0.280912\pi$
$62$	0.698126	−	1.85244i	0.0886621	−	0.235260i
$63$	0.348046	+	0.348046i	0.0438497	+	0.0438497i
$64$	−4.46185	+	6.64017i	−0.557731	+	0.830022i
$65$	−1.83749	−	1.27422i	−0.227912	−	0.158048i
$66$	−5.18544	+	2.34678i	−0.638283	+	0.288869i
$67$	−4.22053	+	4.22053i	−0.515619	+	0.515619i	−0.916243	−	0.400623i	$-0.868794\pi$
$67$	−4.22053	+	4.22053i	−0.515619	+	0.515619i	0.400623	+	0.916243i	$0.368794\pi$
$68$	−0.481251	−	7.44133i	−0.0583602	−	0.902394i
$69$		−	1.78015i		−	0.214304i
$70$	1.41048	+	2.04381i	0.168585	+	0.244282i
$71$			11.5670i			1.37275i	0.727246	+	0.686377i	$0.240800\pi$
$71$			11.5670i			1.37275i	−0.727246	+	0.686377i	$0.759200\pi$
$72$	1.56461	−	0.833685i	0.184391	−	0.0982507i
$73$	−7.67772	+	7.67772i	−0.898610	+	0.898610i	−0.995313	−	0.0967037i	$-0.969170\pi$
$73$	−7.67772	+	7.67772i	−0.898610	+	0.898610i	0.0967037	+	0.995313i	$0.469170\pi$
$74$	−0.691485	−	1.52790i	−0.0803835	−	0.177615i
$75$	−7.01022	−	3.19168i	−0.809470	−	0.368544i
$76$	−8.32136	−	7.31041i	−0.954526	−	0.838562i
$77$	−1.45068	−	1.45068i	−0.165321	−	0.165321i
$78$	2.03865	+	0.768304i	0.230832	+	0.0869933i
$79$	−6.13415			−0.690146			−0.345073	−	0.938576i	$-0.612146\pi$
$79$	−6.13415			−0.690146			−0.345073	+	0.938576i	$0.612146\pi$
$80$	8.52271	−	2.71355i	0.952868	−	0.303384i
$81$	6.72672			0.747414
$82$	0.355249	+	0.133882i	0.0392307	+	0.0147848i
$83$	2.27045	+	2.27045i	0.249214	+	0.249214i	0.820648	−	0.571434i	$-0.193613\pi$
$83$	2.27045	+	2.27045i	0.249214	+	0.249214i	−0.571434	+	0.820648i	$0.693613\pi$
$84$	−1.81767	−	1.59685i	−0.198324	−	0.174230i
$85$	−4.75085	+	6.85096i	−0.515302	+	0.743091i
$86$	3.15185	+	6.96431i	0.339872	+	0.750981i
$87$	1.89794	−	1.89794i	0.203480	−	0.203480i
$88$	−6.52140	+	3.47486i	−0.695184	+	0.370422i
$89$			5.29932i			0.561727i	0.959748	+	0.280863i	$0.0906207\pi$
$89$			5.29932i			0.561727i	−0.959748	+	0.280863i	$0.909379\pi$
$90$	−1.94962	−	0.357452i	−0.205508	−	0.0376788i
$91$			0.785278i			0.0823195i
$92$	−0.149153	−	2.30628i	−0.0155503	−	0.240446i
$93$	1.52482	−	1.52482i	0.158117	−	0.158117i
$94$	14.6777	−	6.64270i	1.51389	−	0.685142i
$95$	2.20582	+	12.1858i	0.226312	+	1.25023i
$96$	−7.41033	+	4.58579i	−0.756313	+	0.468035i
$97$	−3.44319	−	3.44319i	−0.349603	−	0.349603i	0.510359	−	0.859962i	$-0.329513\pi$
$97$	−3.44319	−	3.44319i	−0.349603	−	0.349603i	−0.859962	+	0.510359i	$0.829513\pi$
$98$	−3.18357	+	8.44742i	−0.321589	+	0.853318i
$99$	1.63755			0.164580
$100$	−9.34956	−	3.54764i	−0.934956	−	0.354764i
$101$	13.7679			1.36995			0.684977	−	0.728564i	$-0.259812\pi$
$101$	13.7679			1.36995			0.684977	+	0.728564i	$0.259812\pi$
$102$	2.86458	−	7.60100i	0.283635	−	0.752611i
$103$	−14.1103	−	14.1103i	−1.39033	−	1.39033i	−0.824578	−	0.565749i	$-0.808587\pi$
$103$	−14.1103	−	14.1103i	−1.39033	−	1.39033i	−0.565749	−	0.824578i	$-0.691413\pi$
$104$	2.70557	+	0.824569i	0.265303	+	0.0808556i
$105$	0.481827	+	2.66179i	0.0470215	+	0.259765i
$106$	12.0463	−	5.45183i	1.17004	−	0.529529i
$107$	5.44317	−	5.44317i	0.526211	−	0.526211i	−0.393230	−	0.919440i	$-0.628642\pi$
$107$	5.44317	−	5.44317i	0.526211	−	0.526211i	0.919440	+	0.393230i	$0.128642\pi$
$108$	11.1510	−	0.721166i	1.07301	−	0.0693942i
$109$			13.0292i			1.24797i	0.781437	+	0.623984i	$0.214487\pi$
$109$			13.0292i			1.24797i	−0.781437	+	0.623984i	$0.785513\pi$
$110$	8.12616	+	1.48989i	0.774799	+	0.142055i
$111$		−	1.82688i		−	0.173399i
$112$	−2.48869	−	1.91651i	−0.235159	−	0.181093i
$113$	7.88479	−	7.88479i	0.741739	−	0.741739i	−0.231174	−	0.972912i	$-0.574257\pi$
$113$	7.88479	−	7.88479i	0.741739	−	0.741739i	0.972912	+	0.231174i	$0.0742566\pi$
$114$	−4.97483	−	10.9923i	−0.465935	−	1.02953i
$115$	−1.47242	+	2.12331i	−0.137304	+	0.198000i
$116$	2.29986	−	2.61791i	0.213537	−	0.243066i
$117$	−0.443214	−	0.443214i	−0.0409752	−	0.0409752i
$118$	−16.1145	−	6.07305i	−1.48346	−	0.559069i
$119$	2.92786			0.268397
$120$	9.67678	+	1.13491i	0.883365	+	0.103602i
$121$	4.17458			0.379508
$122$	13.1308	+	4.94858i	1.18881	+	0.448023i
$123$	0.292421	+	0.292421i	0.0263667	+	0.0263667i
$124$	1.84774	−	2.10326i	0.165932	−	0.188878i
$125$	5.72163	+	9.60536i	0.511759	+	0.859129i
$126$	0.287008	+	0.634170i	0.0255687	+	0.0564964i
$127$	−11.0410	+	11.0410i	−0.979728	+	0.979728i	−0.999799	−	0.0200703i	$-0.993611\pi$
$127$	−11.0410	+	11.0410i	−0.979728	+	0.979728i	0.0200703	+	0.999799i	$0.493611\pi$
$128$	−9.21627	+	6.56204i	−0.814611	+	0.580008i
$129$			8.32705i			0.733156i
$130$	−1.79616	−	2.60266i	−0.157533	−	0.228268i
$131$			22.2338i			1.94257i	0.237911	+	0.971287i	$0.423537\pi$
$131$			22.2338i			1.94257i	−0.237911	+	0.971287i	$0.576463\pi$
$132$	−8.03259	+	0.519489i	−0.699147	+	0.0452157i
$133$	3.07523	−	3.07523i	0.266657	−	0.266657i
$134$	−7.69016	+	3.48035i	−0.664329	+	0.300656i
$135$	−10.2663	−	7.11926i	−0.883585	−	0.612729i
$136$	3.07436	−	10.0875i	0.263624	−	0.864999i
$137$	−4.13734	−	4.13734i	−0.353477	−	0.353477i	0.507924	−	0.861402i	$-0.330413\pi$
$137$	−4.13734	−	4.13734i	−0.353477	−	0.353477i	−0.861402	+	0.507924i	$0.830413\pi$
$138$	0.887813	−	2.35576i	0.0755757	−	0.200536i
$139$	12.4175			1.05324			0.526621	−	0.850100i	$-0.323459\pi$
$139$	12.4175			1.05324			0.526621	+	0.850100i	$0.323459\pi$
$140$	0.847259	+	3.40814i	0.0716064	+	0.288040i
$141$	17.5497			1.47795
$142$	−5.76883	+	15.3073i	−0.484110	+	1.28456i
$143$	1.84735	+	1.84735i	0.154483	+	0.154483i
$144$	2.48631	−	0.322944i	0.207193	−	0.0269120i
$145$	−3.83366	+	0.693953i	−0.318368	+	0.0576297i
$146$	−13.9895	+	6.33124i	−1.15778	+	0.523977i
$147$	−6.95345	+	6.95345i	−0.573511	+	0.573511i
$148$	−0.153069	−	2.36682i	−0.0125822	−	0.194552i
$149$		−	2.01151i		−	0.164790i	−0.996600	−	0.0823948i	$-0.973743\pi$
$149$		−	2.01151i		−	0.164790i	0.996600	−	0.0823948i	$-0.0262569\pi$
$150$	−7.68522	−	7.71994i	−0.627495	−	0.630330i
$151$		−	6.76466i		−	0.550500i	−0.961373	−	0.275250i	$-0.911239\pi$
$151$		−	6.76466i		−	0.550500i	0.961373	−	0.275250i	$-0.0887607\pi$
$152$	−7.36619	−	13.8244i	−0.597477	−	1.12131i
$153$	−1.65250	+	1.65250i	−0.133597	+	0.133597i
$154$	−1.19627	−	2.64327i	−0.0963982	−	0.213001i
$155$	−3.08001	+	0.557530i	−0.247392	+	0.0447819i
$156$	2.31469	+	2.03348i	0.185323	+	0.162809i
$157$	14.7248	+	14.7248i	1.17517	+	1.17517i	0.980960	+	0.194211i	$0.0622147\pi$
$157$	14.7248	+	14.7248i	1.17517	+	1.17517i	0.194211	+	0.980960i	$0.437785\pi$
$158$	−8.11766	−	3.05929i	−0.645807	−	0.243384i
$159$	14.4035			1.14227
$160$	12.6319	+	0.659548i	0.998640	+	0.0521419i
$161$	0.907427			0.0715153
$162$	8.90184	+	3.35482i	0.699395	+	0.263580i
$163$	−4.11279	−	4.11279i	−0.322138	−	0.322138i	0.527449	−	0.849587i	$-0.323149\pi$
$163$	−4.11279	−	4.11279i	−0.322138	−	0.322138i	−0.849587	+	0.527449i	$0.823149\pi$
$164$	0.403349	+	0.354347i	0.0314963	+	0.0276698i
$165$	7.39531	+	5.12833i	0.575724	+	0.399240i
$166$	1.87226	+	4.13695i	0.145316	+	0.321089i
$167$	1.64580	−	1.64580i	0.127356	−	0.127356i	−0.640556	−	0.767912i	$-0.721296\pi$
$167$	1.64580	−	1.64580i	0.127356	−	0.127356i	0.767912	+	0.640556i	$0.221296\pi$
$168$	−1.60903	−	3.01972i	−0.124139	−	0.232977i
$169$		−	1.00000i		−	0.0769231i
$170$	−9.70385	+	6.69686i	−0.744251	+	0.513626i
$171$			3.47135i			0.265461i
$172$	0.697699	+	10.7882i	0.0531991	+	0.822590i
$173$	14.6284	−	14.6284i	1.11218	−	1.11218i	0.119320	−	0.992856i	$-0.461929\pi$
$173$	14.6284	−	14.6284i	1.11218	−	1.11218i	0.992856	−	0.119320i	$-0.0380713\pi$
$174$	3.45820	−	1.56508i	0.262166	−	0.118649i
$175$	1.62696	−	3.57345i	0.122986	−	0.270127i
$176$	−10.3631	+	1.34605i	−0.781152	+	0.101463i
$177$	−13.2646	−	13.2646i	−0.997026	−	0.997026i
$178$	−2.64293	+	7.01288i	−0.198096	+	0.525637i
$179$	19.1843			1.43390			0.716952	−	0.697123i	$-0.245537\pi$
$179$	19.1843			1.43390			0.716952	+	0.697123i	$0.245537\pi$
$180$	−2.40176	−	1.44537i	−0.179017	−	0.107732i
$181$	−25.6384			−1.90568			−0.952842	−	0.303466i	$-0.901856\pi$
$181$	−25.6384			−1.90568			−0.952842	+	0.303466i	$0.901856\pi$
$182$	−0.391642	+	1.03920i	−0.0290305	+	0.0770307i
$183$	10.8085	+	10.8085i	0.798990	+	0.798990i
$184$	0.952830	−	3.12641i	0.0702436	−	0.230482i
$185$	−1.51108	+	2.17905i	−0.111097	+	0.160207i
$186$	2.77836	−	1.25741i	0.203719	−	0.0921976i
$187$	6.88774	−	6.88774i	0.503681	−	0.503681i
$188$	22.7367	−	1.47044i	1.65824	−	0.107243i
$189$			4.38747i			0.319142i
$190$	−3.15834	+	17.2262i	−0.229130	+	1.24972i
$191$			5.92335i			0.428599i	0.976768	+	0.214299i	$0.0687468\pi$
$191$			5.92335i			0.428599i	−0.976768	+	0.214299i	$0.931253\pi$
$192$	−12.0936	+	2.37287i	−0.872778	+	0.171247i
$193$	3.85932	−	3.85932i	0.277800	−	0.277800i	−0.554430	−	0.832230i	$-0.687064\pi$
$193$	3.85932	−	3.85932i	0.277800	−	0.277800i	0.832230	+	0.554430i	$0.187064\pi$
$194$	−2.83934	−	6.27379i	−0.203853	−	0.450432i
$195$	−0.613575	−	3.38962i	−0.0439390	−	0.242736i
$196$	−8.42598	+	9.59119i	−0.601855	+	0.685085i
$197$	−5.18774	−	5.18774i	−0.369612	−	0.369612i	0.497724	−	0.867335i	$-0.334169\pi$
$197$	−5.18774	−	5.18774i	−0.369612	−	0.369612i	−0.867335	+	0.497724i	$0.834169\pi$
$198$	2.16705	+	0.816694i	0.154006	+	0.0580399i
$199$	−6.21049			−0.440250			−0.220125	−	0.975472i	$-0.570647\pi$
$199$	−6.21049			−0.440250			−0.220125	+	0.975472i	$0.570647\pi$
$200$	−10.6035	−	9.35770i	−0.749778	−	0.661689i
$201$	−9.19494			−0.648561
$202$	18.2198	+	6.86646i	1.28194	+	0.483123i
$203$	0.967471	+	0.967471i	0.0679031	+	0.0679031i
$204$	7.58170	−	8.63016i	0.530825	−	0.604232i
$205$	−0.106920	−	0.590663i	−0.00746758	−	0.0412537i
$206$	−11.6357	−	25.7101i	−0.810696	−	1.79131i
$207$	−0.512156	+	0.512156i	−0.0355973	+	0.0355973i
$208$	3.16919	+	2.44055i	0.219743	+	0.169221i
$209$		−	14.4689i		−	1.00083i
$210$	−0.689890	+	3.76280i	−0.0476069	+	0.259658i
$211$			13.2561i			0.912586i	0.889830	+	0.456293i	$0.150823\pi$
$211$			13.2561i			0.912586i	−0.889830	+	0.456293i	$0.849177\pi$
$212$	18.6606	−	1.20683i	1.28161	−	0.0828853i
$213$	−12.6001	+	12.6001i	−0.863345	+	0.863345i
$214$	9.91791	−	4.48857i	0.677975	−	0.306832i
$215$	6.88761	−	9.93228i	0.469731	−	0.677376i
$216$	15.1164	+	4.60700i	1.02854	+	0.313466i
$217$	0.777278	+	0.777278i	0.0527650	+	0.0527650i
$218$	−6.49804	+	17.2422i	−0.440103	+	1.16779i
$219$	−16.7269			−1.13030
$220$	10.0107	+	6.02441i	0.674923	+	0.406166i
$221$	−3.72844			−0.250802
$222$	0.911119	−	2.41761i	0.0611503	−	0.162259i
$223$	5.06365	+	5.06365i	0.339087	+	0.339087i	0.856024	−	0.516936i	$-0.172928\pi$
$223$	5.06365	+	5.06365i	0.339087	+	0.339087i	−0.516936	+	0.856024i	$0.672928\pi$
$224$	−2.33760	−	3.77741i	−0.156188	−	0.252389i
$225$	1.09861	+	2.93513i	0.0732406	+	0.195676i
$226$	14.3668	−	6.50199i	0.955663	−	0.432506i
$227$	17.1939	−	17.1939i	1.14120	−	1.14120i	0.152966	−	0.988231i	$-0.451118\pi$
$227$	17.1939	−	17.1939i	1.14120	−	1.14120i	0.988231	−	0.152966i	$-0.0488825\pi$
$228$	−1.10124	−	17.0279i	−0.0729312	−	1.12770i
$229$		−	14.9636i		−	0.988820i	−0.869229	−	0.494410i	$-0.835384\pi$
$229$		−	14.9636i		−	0.988820i	0.869229	−	0.494410i	$-0.164616\pi$
$230$	−3.00750	+	2.07555i	−0.198309	+	0.136858i
$231$		−	3.16050i		−	0.207945i
$232$	4.34916	−	2.31741i	0.285536	−	0.152145i
$233$	−12.2406	+	12.2406i	−0.801906	+	0.801906i	−0.983393	−	0.181488i	$-0.941909\pi$
$233$	−12.2406	+	12.2406i	−0.801906	+	0.801906i	0.181488	+	0.983393i	$0.441909\pi$
$234$	−0.365485	−	0.807574i	−0.0238925	−	0.0527928i
$235$	−20.9328	−	14.5160i	−1.36551	−	0.946921i
$236$	−18.2964	−	16.0736i	−1.19099	−	1.04630i
$237$	−6.68201	−	6.68201i	−0.434043	−	0.434043i
$238$	3.87460	+	1.46021i	0.251153	+	0.0946516i
$239$	−1.22429			−0.0791931			−0.0395965	−	0.999216i	$-0.512607\pi$
$239$	−1.22429			−0.0791931			−0.0395965	+	0.999216i	$0.512607\pi$
$240$	12.2398	+	6.32799i	0.790075	+	0.408470i
$241$	−21.4167			−1.37957			−0.689786	−	0.724014i	$-0.742295\pi$
$241$	−21.4167			−1.37957			−0.689786	+	0.724014i	$0.742295\pi$
$242$	5.52445	+	2.08199i	0.355125	+	0.133836i
$243$	−4.52465	−	4.52465i	−0.290256	−	0.290256i
$244$	14.9087	+	13.0975i	0.954431	+	0.838479i
$245$	14.0453	−	2.54243i	0.897323	−	0.162430i
$246$	0.241137	+	0.532816i	0.0153744	+	0.0339711i
$247$	−3.91611	+	3.91611i	−0.249176	+	0.249176i
$248$	3.49417	−	1.86183i	0.221880	−	0.118227i
$249$			4.94645i			0.313468i
$250$	2.78127	+	15.5648i	0.175903	+	0.984408i
$251$		−	26.5248i		−	1.67423i	−0.547027	−	0.837115i	$-0.684241\pi$
$251$		−	26.5248i		−	1.67423i	0.547027	−	0.837115i	$-0.315759\pi$
$252$	0.0635326	+	0.982372i	0.00400218	+	0.0618836i
$253$	2.13471	−	2.13471i	0.134208	−	0.134208i
$254$	−20.1176	+	9.10466i	−1.26229	+	0.571277i
$255$	−12.6380	+	2.28768i	−0.791422	+	0.143260i
$256$	−15.4691	+	4.08747i	−0.966818	+	0.255467i
$257$	−7.21916	−	7.21916i	−0.450319	−	0.450319i	0.445142	−	0.895460i	$-0.353153\pi$
$257$	−7.21916	−	7.21916i	−0.450319	−	0.450319i	−0.895460	+	0.445142i	$0.853153\pi$
$258$	−4.15296	+	11.0196i	−0.258552	+	0.686053i
$259$	0.931248			0.0578649
$260$	−1.07893	−	4.34004i	−0.0669123	−	0.269158i
$261$	−1.09209			−0.0675986
$262$	−11.0887	+	29.4232i	−0.685060	+	1.81777i
$263$	−16.3159	−	16.3159i	−1.00608	−	1.00608i	−0.999981	−	0.00609825i	$-0.998059\pi$
$263$	−16.3159	−	16.3159i	−1.00608	−	1.00608i	−0.00609825	−	0.999981i	$-0.501941\pi$
$264$	−10.8890	−	3.31863i	−0.670175	−	0.204248i
$265$	−17.1801	−	11.9137i	−1.05537	−	0.731851i
$266$	5.60334	−	2.53591i	0.343563	−	0.155487i
$267$	−5.77261	+	5.77261i	−0.353278	+	0.353278i
$268$	−11.9126	+	0.770417i	−0.727676	+	0.0470607i
$269$			1.48907i			0.0907904i	0.998969	+	0.0453952i	$0.0144547\pi$
$269$			1.48907i			0.0907904i	−0.998969	+	0.0453952i	$0.985545\pi$
$270$	−10.0354	−	14.5414i	−0.610735	−	0.884964i
$271$		−	13.3186i		−	0.809047i	−0.914528	−	0.404523i	$-0.867437\pi$
$271$		−	13.3186i		−	0.809047i	0.914528	−	0.404523i	$-0.132563\pi$
$272$	9.09943	−	11.8161i	0.551734	−	0.716457i
$273$	−0.855413	+	0.855413i	−0.0517719	+	0.0517719i
$274$	−3.41175	−	7.53860i	−0.206112	−	0.455423i
$275$	−4.57909	−	12.2339i	−0.276130	−	0.737730i
$276$	2.34978	−	2.67473i	0.141440	−	0.161000i
$277$	4.36252	+	4.36252i	0.262119	+	0.262119i	0.825914	−	0.563796i	$-0.190659\pi$
$277$	4.36252	+	4.36252i	0.262119	+	0.262119i	−0.563796	+	0.825914i	$0.690659\pi$
$278$	16.4328	+	6.19300i	0.985574	+	0.371432i
$279$	−0.877398			−0.0525284
$280$	−0.578518	+	4.93273i	−0.0345730	+	0.294787i
$281$	−19.2168			−1.14638			−0.573189	−	0.819423i	$-0.694294\pi$
$281$	−19.2168			−1.14638			−0.573189	+	0.819423i	$0.694294\pi$
$282$	23.2245	+	8.75259i	1.38300	+	0.521209i
$283$	8.08334	+	8.08334i	0.480505	+	0.480505i	0.905293	−	0.424788i	$-0.139651\pi$
$283$	8.08334	+	8.08334i	0.480505	+	0.480505i	−0.424788	+	0.905293i	$0.639651\pi$
$284$	−15.2684	+	17.3799i	−0.906014	+	1.03131i
$285$	−10.8713	+	15.6769i	−0.643960	+	0.928622i
$286$	1.52337	+	3.36603i	0.0900788	+	0.199038i
$287$	−0.149061	+	0.149061i	−0.00879881	+	0.00879881i
$288$	3.45134	+	0.812632i	0.203372	+	0.0478848i
$289$		−	3.09874i		−	0.182279i
$290$	−5.41938	−	0.993616i	−0.318237	−	0.0583471i
$291$		−	7.50142i		−	0.439741i
$292$	−21.6706	+	1.40150i	−1.26818	+	0.0820163i
$293$	17.2953	−	17.2953i	1.01040	−	1.01040i	0.0104593	−	0.999945i	$-0.496671\pi$
$293$	17.2953	−	17.2953i	1.01040	−	1.01040i	0.999945	−	0.0104593i	$-0.00332935\pi$
$294$	−12.6698	+	5.73398i	−0.738916	+	0.334412i
$295$	4.85000	+	26.7932i	0.282378	+	1.55996i
$296$	0.977843	−	3.20849i	0.0568359	−	0.186489i
$297$	10.3214	+	10.3214i	0.598911	+	0.598911i
$298$	1.00320	−	2.66195i	0.0581140	−	0.154202i
$299$	−1.15555			−0.0668271
$300$	−6.32010	−	14.0491i	−0.364891	−	0.811124i
$301$	−4.24471			−0.244661
$302$	3.37374	−	8.95205i	0.194137	−	0.515132i
$303$	14.9975	+	14.9975i	0.861584	+	0.861584i
$304$	−2.85343	−	21.9683i	−0.163656	−	1.25997i
$305$	−3.95199	−	21.8322i	−0.226290	−	1.25011i
$306$	−3.01099	+	1.36269i	−0.172127	+	0.0778998i
$307$	13.7867	−	13.7867i	0.786848	−	0.786848i	−0.194128	−	0.980976i	$-0.562188\pi$
$307$	13.7867	−	13.7867i	0.786848	−	0.786848i	0.980976	+	0.194128i	$0.0621878\pi$
$308$	−0.264809	−	4.09460i	−0.0150889	−	0.233312i
$309$		−	30.7410i		−	1.74879i
$310$	−4.35400	−	0.798283i	−0.247290	−	0.0453394i
$311$		−	19.9265i		−	1.12993i	−0.825115	−	0.564965i	$-0.808890\pi$
$311$		−	19.9265i		−	1.12993i	0.825115	−	0.564965i	$-0.191110\pi$
$312$	2.04899	+	3.84542i	0.116001	+	0.217704i
$313$	11.2952	−	11.2952i	0.638445	−	0.638445i	−0.311727	−	0.950172i	$-0.600907\pi$
$313$	11.2952	−	11.2952i	0.638445	−	0.638445i	0.950172	+	0.311727i	$0.100907\pi$
$314$	12.1425	+	26.8299i	0.685239	+	1.51410i
$315$	0.627186	−	0.904434i	0.0353379	−	0.0509591i
$316$	−9.21679	−	8.09705i	−0.518485	−	0.455495i
$317$	2.85332	+	2.85332i	0.160258	+	0.160258i	0.782681	−	0.622423i	$-0.213852\pi$
$317$	2.85332	+	2.85332i	0.160258	+	0.160258i	−0.622423	+	0.782681i	$0.713852\pi$
$318$	19.0610	+	7.18347i	1.06889	+	0.402829i
$319$	4.55191			0.254858
$320$	16.3876	+	7.17273i	0.916092	+	0.400968i
$321$	11.8586			0.661883
$322$	1.20085	+	0.452562i	0.0669207	+	0.0252203i
$323$	14.6010	+	14.6010i	0.812420	+	0.812420i
$324$	10.1071	+	8.87924i	0.561508	+	0.493291i
$325$	−2.07182	+	4.55055i	−0.114924	+	0.252419i
$326$	−3.39150	−	7.49385i	−0.187838	−	0.415046i
$327$	−14.1928	+	14.1928i	−0.784865	+	0.784865i
$328$	0.357050	+	0.670089i	0.0197148	+	0.0369995i
$329$			8.94596i			0.493207i
$330$	7.22896	+	10.4749i	0.397941	+	0.576623i
$331$		−	10.4141i		−	0.572409i	−0.958169	−	0.286205i	$-0.907606\pi$
$331$		−	10.4141i		−	0.572409i	0.958169	−	0.286205i	$-0.0923937\pi$
$332$	0.414448	+	6.40840i	0.0227458	+	0.351707i
$333$	−0.525600	+	0.525600i	−0.0288027	+	0.0288027i
$334$	2.99879	−	1.35717i	0.164086	−	0.0742608i
$335$	10.9675	+	7.60547i	0.599217	+	0.415531i
$336$	−0.623288	−	4.79863i	−0.0340031	−	0.261787i
$337$	−7.46518	−	7.46518i	−0.406654	−	0.406654i	0.473916	−	0.880570i	$-0.342840\pi$
$337$	−7.46518	−	7.46518i	−0.406654	−	0.406654i	−0.880570	+	0.473916i	$0.842840\pi$
$338$	0.498731	−	1.32335i	0.0271274	−	0.0719810i
$339$	17.1780			0.932980
$340$	−16.1816	+	4.02272i	−0.877568	+	0.218163i
$341$	3.65706			0.198041
$342$	−1.73127	+	4.59383i	−0.0936163	+	0.248406i
$343$	−7.43144	−	7.43144i	−0.401260	−	0.401260i
$344$	−4.45709	+	14.6245i	−0.240310	+	0.788502i
$345$	−3.91687	+	0.709016i	−0.210877	+	0.0381722i
$346$	26.6542	−	12.0629i	1.43294	−	0.648507i
$347$	−13.4773	+	13.4773i	−0.723500	+	0.723500i	−0.969316	−	0.245816i	$-0.920944\pi$
$347$	−13.4773	+	13.4773i	−0.723500	+	0.723500i	0.245816	+	0.969316i	$0.420944\pi$
$348$	5.35698	−	0.346450i	0.287164	−	0.0185717i
$349$			11.1418i			0.596405i	0.954503	+	0.298202i	$0.0963870\pi$
$349$			11.1418i			0.596405i	−0.954503	+	0.298202i	$0.903613\pi$
$350$	3.93523	−	3.91753i	0.210347	−	0.209401i
$351$		−	5.58716i		−	0.298220i
$352$	−14.3854	−	3.38711i	−0.766746	−	0.180534i
$353$	−7.91271	+	7.91271i	−0.421151	+	0.421151i	−0.885600	−	0.464449i	$-0.846252\pi$
$353$	−7.91271	+	7.91271i	−0.421151	+	0.421151i	0.464449	+	0.885600i	$0.346252\pi$
$354$	−10.9383	−	24.1692i	−0.581363	−	1.28458i
$355$	25.4511	−	4.60705i	1.35080	−	0.244517i
$356$	−6.99507	+	7.96241i	−0.370738	+	0.422007i
$357$	3.18935	+	3.18935i	0.168799	+	0.168799i
$358$	25.3877	+	9.56781i	1.34178	+	0.505674i
$359$	−16.1308			−0.851351			−0.425675	−	0.904876i	$-0.639963\pi$
$359$	−16.1308			−0.851351			−0.425675	+	0.904876i	$0.639963\pi$
$360$	−2.45753	−	3.11057i	−0.129523	−	0.163941i
$361$	11.6718			0.614305
$362$	−33.9286	−	12.7866i	−1.78325	−	0.672051i
$363$	4.54742	+	4.54742i	0.238678	+	0.238678i
$364$	−1.03656	+	1.17991i	−0.0543307	+	0.0618440i
$365$	19.9513	+	13.8354i	1.04430	+	0.724178i
$366$	8.91298	+	19.6941i	0.465889	+	1.02943i
$367$	−20.5903	+	20.5903i	−1.07480	+	1.07480i	−0.0778383	+	0.996966i	$0.524802\pi$
$367$	−20.5903	+	20.5903i	−1.07480	+	1.07480i	−0.996966	+	0.0778383i	$0.975198\pi$
$368$	2.82017	−	3.66215i	0.147012	−	0.190903i
$369$		−	0.168262i		−	0.00875935i
$370$	−3.08645	+	2.13003i	−0.160457	+	0.110735i
$371$			7.34218i			0.381187i
$372$	4.30386	−	0.278342i	0.223145	−	0.0144314i
$373$	0.929154	−	0.929154i	0.0481098	−	0.0481098i	−0.682643	−	0.730752i	$-0.739169\pi$
$373$	0.929154	−	0.929154i	0.0481098	−	0.0481098i	0.730752	+	0.682643i	$0.239169\pi$
$374$	12.5500	−	5.67980i	0.648948	−	0.293695i
$375$	−4.23058	+	16.6959i	−0.218466	+	0.862171i
$376$	30.8220	+	9.39356i	1.58953	+	0.484436i
$377$	−1.23201	−	1.23201i	−0.0634518	−	0.0634518i
$378$	−2.18817	+	5.80618i	−0.112547	+	0.298638i
$379$	0.239279			0.0122909			0.00614547	−	0.999981i	$-0.498044\pi$
$379$	0.239279			0.0122909			0.00614547	+	0.999981i	$0.498044\pi$
$380$	−12.7708	+	21.2212i	−0.655131	+	1.08863i
$381$	−24.0541			−1.23233
$382$	−2.95416	+	7.83869i	−0.151148	+	0.401062i
$383$	21.2103	+	21.2103i	1.08379	+	1.08379i	0.996152	+	0.0876426i	$0.0279334\pi$
$383$	21.2103	+	21.2103i	1.08379	+	1.08379i	0.0876426	+	0.996152i	$0.472067\pi$
$384$	−17.1875	−	2.89128i	−0.877096	−	0.147545i
$385$	−2.61416	+	3.76975i	−0.133230	+	0.192124i
$386$	7.03201	−	3.18249i	0.357920	−	0.161984i
$387$	2.39573	−	2.39573i	0.121782	−	0.121782i
$388$	−0.628522	−	9.71851i	−0.0319084	−	0.493383i
$389$		−	19.1329i		−	0.970077i	−0.874493	−	0.485039i	$-0.838806\pi$
$389$		−	19.1329i		−	0.970077i	0.874493	−	0.485039i	$-0.161194\pi$
$390$	0.878530	−	4.79168i	0.0444861	−	0.242636i
$391$			4.30839i			0.217885i
$392$	−15.9340	+	8.49026i	−0.804787	+	0.428823i
$393$	−24.2195	+	24.2195i	−1.22171	+	1.22171i
$394$	−4.27794	−	9.45251i	−0.215519	−	0.476211i
$395$	2.44318	+	13.4970i	0.122930	+	0.679110i
$396$	2.46047	+	2.16155i	0.123643	+	0.108622i
$397$	11.7462	+	11.7462i	0.589526	+	0.589526i	0.937503	−	0.347977i	$-0.113131\pi$
$397$	11.7462	+	11.7462i	0.589526	+	0.589526i	−0.347977	+	0.937503i	$0.613131\pi$
$398$	−8.21868	−	3.09736i	−0.411965	−	0.155257i
$399$	6.69978			0.335408
$400$	−9.36517	−	17.6718i	−0.468259	−	0.883591i
$401$	25.7092			1.28385			0.641927	−	0.766766i	$-0.278135\pi$
$401$	25.7092			1.28385			0.641927	+	0.766766i	$0.278135\pi$
$402$	−12.1682	−	4.58580i	−0.606893	−	0.228719i
$403$	−0.989812	−	0.989812i	−0.0493060	−	0.0493060i
$404$	20.6867	+	18.1735i	1.02920	+	0.904167i
$405$	−2.67919	−	14.8009i	−0.133130	−	0.735461i
$406$	0.797800	+	1.76281i	0.0395941	+	0.0874870i
$407$	2.19074	−	2.19074i	0.108591	−	0.108591i
$408$	14.3374	−	7.63954i	0.709807	−	0.378214i
$409$			23.0564i			1.14007i	0.821621	+	0.570034i	$0.193070\pi$
$409$			23.0564i			1.14007i	−0.821621	+	0.570034i	$0.806930\pi$
$410$	0.153090	−	0.834981i	0.00756055	−	0.0412368i
$411$		−	9.01372i		−	0.444614i
$412$	−2.57570	−	39.8267i	−0.126895	−	1.96212i
$413$	6.76160	−	6.76160i	0.332716	−	0.332716i
$414$	−0.933192	+	0.422336i	−0.0458639	+	0.0207567i
$415$	4.09139	−	5.89998i	0.200838	−	0.289619i
$416$	2.97678	+	4.81028i	0.145949	+	0.235843i
$417$	13.5266	+	13.5266i	0.662399	+	0.662399i
$418$	7.21606	−	19.1474i	0.352949	−	0.936531i
$419$	−15.1893			−0.742048			−0.371024	−	0.928623i	$-0.620993\pi$
$419$	−15.1893			−0.742048			−0.371024	+	0.928623i	$0.620993\pi$
$420$	−2.78959	+	4.63545i	−0.136118	+	0.226187i
$421$	2.77524			0.135257			0.0676286	−	0.997711i	$-0.478457\pi$
$421$	2.77524			0.135257			0.0676286	+	0.997711i	$0.478457\pi$
$422$	−6.61121	+	17.5425i	−0.321829	+	0.853955i
$423$	−5.04914	−	5.04914i	−0.245497	−	0.245497i
$424$	25.2964	+	7.70954i	1.22850	+	0.374408i
$425$	16.9665	+	7.72467i	0.822995	+	0.374701i
$426$	−22.9585	+	10.3904i	−1.11234	+	0.503414i
$427$	−5.50964	+	5.50964i	−0.266630	+	0.266630i
$428$	15.3635	−	0.993598i	0.742623	−	0.0480274i
$429$			4.02468i			0.194314i
$430$	14.0683	−	9.70886i	0.678433	−	0.468203i
$431$		−	19.7282i		−	0.950275i	−0.879911	−	0.475138i	$-0.842398\pi$
$431$		−	19.7282i		−	0.950275i	0.879911	−	0.475138i	$-0.157602\pi$
$432$	17.7067	+	13.6357i	0.851916	+	0.656048i
$433$	13.7591	−	13.7591i	0.661220	−	0.661220i	−0.294447	−	0.955668i	$-0.595136\pi$
$433$	13.7591	−	13.7591i	0.661220	−	0.661220i	0.955668	+	0.294447i	$0.0951355\pi$
$434$	0.640962	+	1.41627i	0.0307672	+	0.0679830i
$435$	−4.93198	−	3.42012i	−0.236470	−	0.163982i
$436$	−17.1984	+	19.5768i	−0.823655	+	0.937558i
$437$	4.52525	+	4.52525i	0.216472	+	0.216472i
$438$	−22.1356	−	8.34220i	−1.05768	−	0.398606i
$439$	21.2804			1.01566			0.507828	−	0.861459i	$-0.330449\pi$
$439$	21.2804			1.01566			0.507828	+	0.861459i	$0.330449\pi$
$440$	10.2432	+	12.9651i	0.488325	+	0.618087i
$441$	4.00107			0.190527
$442$	−4.93405	−	1.85949i	−0.234689	−	0.0884468i
$443$	5.32319	+	5.32319i	0.252912	+	0.252912i	0.822164	−	0.569251i	$-0.192767\pi$
$443$	5.32319	+	5.32319i	0.252912	+	0.252912i	−0.569251	+	0.822164i	$0.692767\pi$
$444$	2.41147	−	2.74495i	0.114443	−	0.130269i
$445$	11.6601	−	2.11067i	0.552744	−	0.100055i
$446$	4.17561	+	9.22641i	0.197721	+	0.436883i
$447$	2.19117	−	2.19117i	0.103639	−	0.103639i
$448$	−1.20957	−	6.16468i	−0.0571467	−	0.291254i
$449$			7.92418i			0.373965i	0.982363	+	0.186983i	$0.0598708\pi$
$449$			7.92418i			0.373965i	−0.982363	+	0.186983i	$0.940129\pi$
$450$	−0.00999041	+	4.43213i	−0.000470952	+	0.208933i
$451$			0.701327i			0.0330242i
$452$	22.2551	−	1.43929i	1.04679	−	0.0676987i
$453$	7.36883	−	7.36883i	0.346218	−	0.346218i
$454$	31.3287	−	14.1785i	1.47033	−	0.665429i
$455$	1.72786	−	0.312769i	0.0810031	−	0.0146629i
$456$	7.03499	−	23.0831i	0.329444	−	1.08097i
$457$	29.0379	+	29.0379i	1.35834	+	1.35834i	0.875970	+	0.482366i	$0.160222\pi$
$457$	29.0379	+	29.0379i	1.35834	+	1.35834i	0.482366	+	0.875970i	$0.339778\pi$
$458$	7.46279	−	19.8021i	0.348713	−	0.925292i
$459$	−20.8314			−0.972325
$460$	−5.01513	+	1.24675i	−0.233831	+	0.0581302i
$461$	−2.07249			−0.0965253			−0.0482626	−	0.998835i	$-0.515368\pi$
$461$	−2.07249			−0.0965253			−0.0482626	+	0.998835i	$0.515368\pi$
$462$	1.57624	−	4.18246i	0.0733331	−	0.194586i
$463$	−3.97424	−	3.97424i	−0.184699	−	0.184699i	0.608701	−	0.793400i	$-0.291691\pi$
$463$	−3.97424	−	3.97424i	−0.184699	−	0.184699i	−0.793400	+	0.608701i	$0.791691\pi$
$464$	6.91125	−	0.897692i	0.320847	−	0.0416743i
$465$	−3.96241	−	2.74776i	−0.183752	−	0.127424i
$466$	−22.3033	+	10.0939i	−1.03318	+	0.467589i
$467$	−1.80715	+	1.80715i	−0.0836251	+	0.0836251i	−0.747682	−	0.664057i	$-0.768833\pi$
$467$	−1.80715	+	1.80715i	−0.0836251	+	0.0836251i	0.664057	+	0.747682i	$0.268833\pi$
$468$	−0.0809046	−	1.25099i	−0.00373981	−	0.0578268i
$469$		−	4.68711i		−	0.216431i
$470$	−20.4620	−	29.6497i	−0.943841	−	1.36764i
$471$			32.0799i			1.47816i
$472$	−16.1962	−	30.3960i	−0.745492	−	1.39909i
$473$	−9.98559	+	9.98559i	−0.459138	+	0.459138i
$474$	−5.51014	−	12.1752i	−0.253089	−	0.559225i
$475$	25.9339	−	9.70698i	1.18993	−	0.445387i
$476$	4.39922	+	3.86476i	0.201638	+	0.177141i
$477$	−4.14396	−	4.14396i	−0.189739	−	0.189739i
$478$	−1.62018	−	0.610593i	−0.0741052	−	0.0279279i
$479$	−26.5874			−1.21481			−0.607404	−	0.794393i	$-0.707789\pi$
$479$	−26.5874			−1.21481			−0.607404	+	0.794393i	$0.707789\pi$
$480$	13.0416	+	14.4785i	0.595266	+	0.660852i
$481$	−1.18588			−0.0540716
$482$	−28.3419	−	10.6812i	−1.29094	−	0.486514i
$483$	0.988471	+	0.988471i	0.0449770	+	0.0449770i
$484$	6.27246	+	5.51043i	0.285112	+	0.250474i
$485$	−6.20469	+	8.94748i	−0.281741	+	0.406284i
$486$	−3.73113	−	8.24430i	−0.169248	−	0.373969i
$487$	6.65587	−	6.65587i	0.301606	−	0.301606i	−0.540036	−	0.841642i	$-0.681589\pi$
$487$	6.65587	−	6.65587i	0.301606	−	0.301606i	0.841642	+	0.540036i	$0.181589\pi$
$488$	13.1974	+	24.7680i	0.597417	+	1.12119i
$489$		−	8.96022i		−	0.405195i
$490$	19.8549	+	3.64030i	0.896954	+	0.164452i
$491$			10.2609i			0.463069i	0.972827	+	0.231534i	$0.0743746\pi$
$491$			10.2609i			0.463069i	−0.972827	+	0.231534i	$0.925625\pi$
$492$	0.0533787	+	0.825367i	0.00240650	+	0.0372104i
$493$	−4.59348	+	4.59348i	−0.206880	+	0.206880i
$494$	−7.13548	+	3.22932i	−0.321041	+	0.145294i
$495$	−0.652220	−	3.60311i	−0.0293151	−	0.161948i
$496$	5.55258	−	0.721216i	0.249318	−	0.0323836i
$497$	−6.42289	−	6.42289i	−0.288106	−	0.288106i
$498$	−2.46695	+	6.54591i	−0.110546	+	0.293329i
$499$	−22.7084			−1.01657			−0.508284	−	0.861190i	$-0.669720\pi$
$499$	−22.7084			−1.01657			−0.508284	+	0.861190i	$0.669720\pi$
$500$	−4.08206	+	21.9849i	−0.182555	+	0.983196i
$501$	3.58558			0.160192
$502$	13.2287	−	35.1017i	0.590427	−	1.56667i
$503$	−22.8714	−	22.8714i	−1.01979	−	1.01979i	−0.999800	−	0.0199855i	$-0.993638\pi$
$503$	−22.8714	−	22.8714i	−1.01979	−	1.01979i	−0.0199855	−	0.999800i	$-0.506362\pi$
$504$	−0.405863	+	1.33171i	−0.0180786	+	0.0593192i
$505$	−5.48362	−	30.2936i	−0.244018	−	1.34805i
$506$	3.88962	−	1.76033i	0.172915	−	0.0782562i
$507$	1.08931	−	1.08931i	0.0483780	−	0.0483780i
$508$	−31.1635	+	2.01543i	−1.38266	+	0.0894200i
$509$		−	13.0663i		−	0.579152i	−0.957155	−	0.289576i	$-0.906486\pi$
$509$		−	13.0663i		−	0.579152i	0.957155	−	0.289576i	$-0.0935143\pi$
$510$	−17.8655	−	3.27554i	−0.791097	−	0.145044i
$511$		−	8.52650i		−	0.377190i
$512$	−22.5096	−	2.30573i	−0.994795	−	0.101900i
$513$	−21.8799	+	21.8799i	−0.966021	+	0.966021i
$514$	−5.95309	−	13.1539i	−0.262580	−	0.580195i
$515$	−25.4270	+	36.6670i	−1.12045	+	1.61574i
$516$	−10.9917	+	12.5117i	−0.483881	+	0.550797i
$517$	21.0452	+	21.0452i	0.925567	+	0.925567i
$518$	1.23237	+	0.464442i	0.0541473	+	0.0204064i
$519$	31.8697			1.39893
$520$	0.736704	−	6.28150i	0.0323066	−	0.275462i
$521$	−7.80199			−0.341811			−0.170906	−	0.985287i	$-0.554669\pi$
$521$	−7.80199			−0.341811			−0.170906	+	0.985287i	$0.554669\pi$
$522$	−1.44522	−	0.544658i	−0.0632556	−	0.0238390i
$523$	−21.0008	−	21.0008i	−0.918299	−	0.918299i	0.0786066	−	0.996906i	$-0.474953\pi$
$523$	−21.0008	−	21.0008i	−0.918299	−	0.918299i	−0.996906	+	0.0786066i	$0.974953\pi$
$524$	−29.3485	+	33.4070i	−1.28209	+	1.45939i
$525$	5.66487	−	2.12034i	0.247235	−	0.0925392i
$526$	−13.4545	−	29.7289i	−0.586642	−	1.29624i
$527$	−3.69045	+	3.69045i	−0.160759	+	0.160759i
$528$	−12.7550	−	9.82243i	−0.555089	−	0.427466i
$529$		−	21.6647i		−	0.941944i
$530$	−16.7937	−	24.3343i	−0.729470	−	1.05701i
$531$			7.63255i			0.331224i
$532$	8.67994	−	0.561355i	0.376323	−	0.0243378i
$533$	0.189820	−	0.189820i	0.00822200	−	0.00822200i
$534$	−10.5182	+	4.76023i	−0.455166	+	0.205995i
$535$	−14.1446	−	9.80869i	−0.611525	−	0.424067i
$536$	−16.1488	−	4.92163i	−0.697521	−	0.212582i
$537$	20.8977	+	20.8977i	0.901803	+	0.901803i
$538$	−0.742647	+	1.97057i	−0.0320178	+	0.0849574i
$539$	−16.6768			−0.718320
$540$	−6.02814	−	24.2485i	−0.259410	−	1.04349i
$541$	−45.7567			−1.96723			−0.983616	−	0.180276i	$-0.942301\pi$
$541$	−45.7567			−1.96723			−0.983616	+	0.180276i	$0.942301\pi$
$542$	6.64239	−	17.6252i	0.285315	−	0.757068i
$543$	−27.9282	−	27.9282i	−1.19851	−	1.19851i
$544$	17.9348	−	11.0988i	0.768949	−	0.475855i
$545$	28.6682	−	5.18940i	1.22801	−	0.222289i
$546$	−1.55863	+	0.705394i	−0.0667034	+	0.0301881i
$547$	−1.26509	+	1.26509i	−0.0540915	+	0.0540915i	−0.733635	−	0.679544i	$-0.762178\pi$
$547$	−1.26509	+	1.26509i	−0.0540915	+	0.0540915i	0.679544	+	0.733635i	$0.262178\pi$
$548$	−0.755233	−	11.6778i	−0.0322620	−	0.498850i
$549$		−	6.21933i		−	0.265434i
$550$	0.0416408	−	18.4735i	0.00177557	−	0.787711i
$551$			9.64937i			0.411077i
$552$	4.44357	−	2.36771i	0.189131	−	0.100776i
$553$	3.40615	−	3.40615i	0.144844	−	0.144844i
$554$	3.59744	+	7.94889i	0.152841	+	0.337716i
$555$	−4.01969	+	0.727629i	−0.170627	+	0.0308861i
$556$	18.6578	+	16.3911i	0.791266	+	0.695137i
$557$	9.55340	+	9.55340i	0.404790	+	0.404790i	0.879917	−	0.475127i	$-0.157598\pi$
$557$	9.55340	+	9.55340i	0.404790	+	0.404790i	−0.475127	+	0.879917i	$0.657598\pi$
$558$	−1.16111	−	0.437585i	−0.0491536	−	0.0185245i
$559$	5.40535			0.228622
$560$	−3.22569	+	6.23922i	−0.136310	+	0.263655i
$561$	15.0058			0.633545
$562$	−25.4306	−	9.58400i	−1.07273	−	0.404277i
$563$	−15.7377	−	15.7377i	−0.663264	−	0.663264i	0.292884	−	0.956148i	$-0.405385\pi$
$563$	−15.7377	−	15.7377i	−0.663264	−	0.663264i	−0.956148	+	0.292884i	$0.905385\pi$
$564$	26.3691	+	23.1656i	1.11034	+	0.975446i
$565$	−20.4894	−	14.2085i	−0.861996	−	0.597758i
$566$	6.66572	+	14.7285i	0.280181	+	0.619086i
$567$	−3.73518	+	3.73518i	−0.156863	+	0.156863i
$568$	−28.8734	+	15.3849i	−1.21150	+	0.645537i
$569$			34.6969i			1.45457i	0.686336	+	0.727285i	$0.259218\pi$
$569$			34.6969i			1.45457i	−0.686336	+	0.727285i	$0.740782\pi$
$570$	−22.2051	+	15.3243i	−0.930071	+	0.641865i
$571$			31.8445i			1.33265i	0.745661	+	0.666325i	$0.232134\pi$
$571$			31.8445i			1.33265i	−0.745661	+	0.666325i	$0.767866\pi$
$572$	0.337216	+	5.21421i	0.0140997	+	0.218017i
$573$	−6.45238	+	6.45238i	−0.269552	+	0.269552i
$574$	−0.271602	+	0.122919i	−0.0113365	+	0.00513056i
$575$	5.25839	+	2.39409i	0.219290	+	0.0998406i
$576$	4.16206	+	2.79669i	0.173419	+	0.116529i
$577$	−18.9584	−	18.9584i	−0.789250	−	0.789250i	0.192121	−	0.981371i	$-0.438463\pi$
$577$	−18.9584	−	18.9584i	−0.789250	−	0.789250i	−0.981371	+	0.192121i	$0.938463\pi$
$578$	1.54544	−	4.10073i	0.0642817	−	0.170568i
$579$	8.40801			0.349425
$580$	−6.67622	−	4.01772i	−0.277215	−	0.166827i
$581$	−2.52145			−0.104607
$582$	3.74119	−	9.92703i	0.155077	−	0.411489i
$583$	17.2723	+	17.2723i	0.715347	+	0.715347i
$584$	−29.3769	−	8.95312i	−1.21562	−	0.370483i
$585$	−0.798681	+	1.15174i	−0.0330214	+	0.0476185i
$586$	31.5136	−	14.2622i	1.30181	−	0.589164i
$587$	25.5124	−	25.5124i	1.05301	−	1.05301i	0.0544948	−	0.998514i	$-0.482645\pi$
$587$	25.5124	−	25.5124i	1.05301	−	1.05301i	0.998514	−	0.0544948i	$-0.0173548\pi$
$588$	−19.6263	+	1.26929i	−0.809376	+	0.0523444i
$589$			7.75242i			0.319433i
$590$	−6.94432	+	37.8758i	−0.285893	+	1.55932i
$591$		−	11.3021i		−	0.464908i
$592$	2.89420	−	3.75828i	0.118951	−	0.154465i
$593$	−24.8373	+	24.8373i	−1.01994	+	1.01994i	−0.0201477	+	0.999797i	$0.506414\pi$
$593$	−24.8373	+	24.8373i	−1.01994	+	1.01994i	−0.999797	+	0.0201477i	$0.993586\pi$
$594$	8.51131	+	18.8065i	0.349223	+	0.771642i
$595$	−1.16614	−	6.44220i	−0.0478071	−	0.264105i
$596$	2.65519	−	3.02237i	0.108761	−	0.123801i
$597$	−6.76516	−	6.76516i	−0.276880	−	0.276880i
$598$	−1.52920	−	0.576308i	−0.0625337	−	0.0235670i
$599$	2.06094			0.0842077			0.0421039	−	0.999113i	$-0.486594\pi$
$599$	2.06094			0.0842077			0.0421039	+	0.999113i	$0.486594\pi$
$600$	−1.35703	−	21.7439i	−0.0554004	−	0.887692i
$601$	38.4787			1.56958			0.784789	−	0.619763i	$-0.212771\pi$
$601$	38.4787			1.56958			0.784789	+	0.619763i	$0.212771\pi$
$602$	−5.61725	−	2.11697i	−0.228942	−	0.0862811i
$603$	2.64543	+	2.64543i	0.107730	+	0.107730i
$604$	8.92932	−	10.1641i	0.363329	−	0.413573i
$605$	−1.66270	−	9.18538i	−0.0675984	−	0.373439i
$606$	12.3673	+	27.3267i	0.502388	+	1.11007i
$607$	−5.25189	+	5.25189i	−0.213168	+	0.213168i	−0.805612	−	0.592444i	$-0.798163\pi$
$607$	−5.25189	+	5.25189i	−0.213168	+	0.213168i	0.592444	+	0.805612i	$0.298163\pi$
$608$	7.18017	−	30.4950i	0.291194	−	1.23673i
$609$			2.10775i			0.0854105i
$610$	5.65853	−	30.8628i	0.229107	−	1.24960i
$611$		−	11.3921i		−	0.460875i
$612$	−4.66423	+	0.301648i	−0.188540	+	0.0121934i
$613$	11.0862	−	11.0862i	0.447767	−	0.447767i	−0.446844	−	0.894612i	$-0.647452\pi$
$613$	11.0862	−	11.0862i	0.447767	−	0.447767i	0.894612	+	0.446844i	$0.147452\pi$
$614$	25.1205	−	11.3688i	1.01378	−	0.458809i
$615$	0.526948	−	0.759885i	0.0212486	−	0.0306415i
$616$	1.69167	−	5.55068i	0.0681592	−	0.223643i
$617$	−5.58285	−	5.58285i	−0.224757	−	0.224757i	0.585741	−	0.810498i	$-0.300804\pi$
$617$	−5.58285	−	5.58285i	−0.224757	−	0.224757i	−0.810498	+	0.585741i	$0.800804\pi$
$618$	15.3315	−	40.6812i	0.616722	−	1.63644i
$619$	19.7859			0.795261			0.397630	−	0.917546i	$-0.369833\pi$
$619$	19.7859			0.795261			0.397630	+	0.917546i	$0.369833\pi$
$620$	−5.36376	−	3.22788i	−0.215414	−	0.129635i
$621$	−6.45623			−0.259080
$622$	9.93797	−	26.3699i	0.398476	−	1.05734i
$623$	−2.94258	−	2.94258i	−0.117892	−	0.117892i
$624$	0.793716	+	6.11075i	0.0317741	+	0.244626i
$625$	18.8559	−	16.4151i	0.754236	−	0.656604i
$626$	20.5809	−	9.31433i	0.822578	−	0.372275i
$627$	15.7611	−	15.7611i	0.629437	−	0.629437i
$628$	2.68788	+	41.5613i	0.107258	+	1.65848i
$629$			4.42149i			0.176297i
$630$	1.28106	−	0.884090i	0.0510386	−	0.0352230i
$631$		−	45.3821i		−	1.80663i	−0.428976	−	0.903316i	$-0.641125\pi$
$631$		−	45.3821i		−	1.80663i	0.428976	−	0.903316i	$-0.358875\pi$
$632$	−8.15883	−	15.3120i	−0.324541	−	0.609077i
$633$	−14.4400	+	14.4400i	−0.573938	+	0.573938i
$634$	2.35292	+	5.19899i	0.0934462	+	0.206478i
$635$	28.6911	+	19.8960i	1.13857	+	0.789551i
$636$	21.6418	+	19.0126i	0.858153	+	0.753897i
$637$	4.51370	+	4.51370i	0.178839	+	0.178839i
$638$	6.02379	+	2.27018i	0.238484	+	0.0898772i
$639$	7.25021			0.286814
$640$	18.1093	+	17.6650i	0.715832	+	0.698272i
$641$	−25.1139			−0.991939			−0.495969	−	0.868340i	$-0.665187\pi$
$641$	−25.1139			−0.991939			−0.495969	+	0.868340i	$0.665187\pi$
$642$	15.6931	+	5.91425i	0.619359	+	0.233417i
$643$	−8.77643	−	8.77643i	−0.346109	−	0.346109i	0.512549	−	0.858658i	$-0.328701\pi$
$643$	−8.77643	−	8.77643i	−0.346109	−	0.346109i	−0.858658	+	0.512549i	$0.828701\pi$
$644$	1.36344	+	1.19780i	0.0537271	+	0.0471999i
$645$	18.3221	−	3.31659i	0.721432	−	0.130591i
$646$	12.0403	+	26.6042i	0.473720	+	1.04673i
$647$	−8.86854	+	8.86854i	−0.348658	+	0.348658i	−0.859610	−	0.510951i	$-0.829293\pi$
$647$	−8.86854	+	8.86854i	−0.348658	+	0.348658i	0.510951	+	0.859610i	$0.329293\pi$
$648$	8.94698	+	16.7911i	0.351471	+	0.659618i
$649$		−	31.8131i		−	1.24877i
$650$	−5.01126	+	4.98872i	−0.196558	+	0.195674i
$651$			1.69340i			0.0663694i
$652$	−0.750750	−	11.6085i	−0.0294016	−	0.454623i
$653$	−29.2512	+	29.2512i	−1.14469	+	1.14469i	−0.157104	+	0.987582i	$0.550216\pi$
$653$	−29.2512	+	29.2512i	−1.14469	+	1.14469i	−0.987582	+	0.157104i	$0.949784\pi$
$654$	−25.8605	+	11.7037i	−1.01123	+	0.457652i
$655$	48.9212	−	8.85552i	1.91151	−	0.346014i
$656$	0.138310	+	1.06484i	0.00540010	+	0.0415749i
$657$	4.81239	+	4.81239i	0.187749	+	0.187749i
$658$	−4.46162	+	11.8387i	−0.173932	+	0.461520i
$659$	9.65978			0.376292			0.188146	−	0.982141i	$-0.439752\pi$
$659$	9.65978			0.376292			0.188146	+	0.982141i	$0.439752\pi$
$660$	4.34234	+	17.4673i	0.169026	+	0.679913i
$661$	−17.3904			−0.676407			−0.338203	−	0.941073i	$-0.609819\pi$
$661$	−17.3904			−0.676407			−0.338203	+	0.941073i	$0.609819\pi$
$662$	5.19382	−	13.7815i	0.201863	−	0.535634i
$663$	−4.06143	−	4.06143i	−0.157733	−	0.157733i
$664$	−2.64761	+	8.68729i	−0.102747	+	0.337132i
$665$	−7.99130	−	5.54163i	−0.309889	−	0.214895i
$666$	−0.957689	+	0.433423i	−0.0371097	+	0.0167948i
$667$	−1.42365	+	1.42365i	−0.0551239	+	0.0551239i
$668$	4.64532	−	0.300425i	0.179733	−	0.0116238i
$669$			11.0318i			0.426514i
$670$	10.7208	+	15.5345i	0.414179	+	0.600152i
$671$			25.9226i			1.00073i
$672$	1.56840	−	6.66115i	0.0605022	−	0.256959i
$673$	−5.95062	+	5.95062i	−0.229380	+	0.229380i	−0.812433	−	0.583054i	$-0.801858\pi$
$673$	−5.95062	+	5.95062i	−0.229380	+	0.229380i	0.583054	+	0.812433i	$0.301858\pi$
$674$	−6.15597	−	13.6022i	−0.237119	−	0.523937i
$675$	−11.5756	+	25.4247i	−0.445545	+	0.978596i
$676$	1.32000	−	1.50254i	0.0507690	−	0.0577898i
$677$	7.68011	+	7.68011i	0.295171	+	0.295171i	0.839119	−	0.543948i	$-0.183071\pi$
$677$	7.68011	+	7.68011i	0.295171	+	0.295171i	−0.543948	+	0.839119i	$0.683071\pi$
$678$	22.7326	+	8.56719i	0.873039	+	0.329021i
$679$	3.82384			0.146745
$680$	−23.4202	−	2.74676i	−0.898124	−	0.105333i
$681$	37.4590			1.43543
$682$	4.83959	+	1.82389i	0.185317	+	0.0698403i
$683$	26.3784	+	26.3784i	1.00934	+	1.00934i	0.999956	+	0.00938591i	$0.00298767\pi$
$683$	26.3784	+	26.3784i	1.00934	+	1.00934i	0.00938591	+	0.999956i	$0.497012\pi$
$684$	−4.58216	+	5.21583i	−0.175203	+	0.199432i
$685$	−7.45557	+	10.7513i	−0.284863	+	0.410786i
$686$	−6.12814	−	13.5407i	−0.233974	−	0.516987i
$687$	16.3000	−	16.3000i	0.621883	−	0.621883i
$688$	−13.1920	+	17.1306i	−0.502941	+	0.653097i
$689$		−	9.34978i		−	0.356198i
$690$	−5.53702	−	1.01518i	−0.210791	−	0.0386474i
$691$			40.5369i			1.54210i	0.636777	+	0.771048i	$0.280267\pi$
$691$			40.5369i			1.54210i	−0.636777	+	0.771048i	$0.719733\pi$
$692$	41.2891	−	2.67027i	1.56957	−	0.101509i
$693$	−0.909289	+	0.909289i	−0.0345410	+	0.0345410i
$694$	−24.5568	+	11.1137i	−0.932164	+	0.421871i
$695$	−4.94579	−	27.3224i	−0.187605	−	1.03640i
$696$	7.26197	+	2.21321i	0.275264	+	0.0838917i
$697$	−0.707731	−	0.707731i	−0.0268072	−	0.0268072i
$698$	−5.55674	+	14.7445i	−0.210326	+	0.558087i
$699$	−26.6676			−1.00866
$700$	7.16150	−	3.22166i	0.270679	−	0.121767i
$701$	−21.9492			−0.829009			−0.414504	−	0.910047i	$-0.636045\pi$
$701$	−21.9492			−0.829009			−0.414504	+	0.910047i	$0.636045\pi$
$702$	2.78649	−	7.39379i	0.105169	−	0.279061i
$703$	4.64405	+	4.64405i	0.175154	+	0.175154i
$704$	−17.3478	−	11.6568i	−0.653819	−	0.439333i
$705$	−6.98991	−	38.6149i	−0.263255	−	1.45432i
$706$	−14.4176	+	6.52501i	−0.542615	+	0.245572i
$707$	−7.64496	+	7.64496i	−0.287518	+	0.287518i
$708$	−2.42132	−	37.4396i	−0.0909988	−	1.40707i
$709$			1.71169i			0.0642840i	0.999483	+	0.0321420i	$0.0102329\pi$
$709$			1.71169i			0.0642840i	−0.999483	+	0.0321420i	$0.989767\pi$
$710$	35.9785	+	6.59646i	1.35025	+	0.247561i
$711$			3.84489i			0.144194i
$712$	−13.2281	+	7.04844i	−0.495743	+	0.264151i
$713$	−1.14378	+	1.14378i	−0.0428348	+	0.0428348i
$714$	2.63002	+	5.81128i	0.0984260	+	0.217482i
$715$	3.32896	−	4.80053i	0.124496	−	0.179530i
$716$	28.8251	+	25.3232i	1.07725	+	0.946373i
$717$	−1.33364	−	1.33364i	−0.0498057	−	0.0498057i
$718$	−21.3468	−	8.04492i	−0.796654	−	0.300234i
$719$	−16.1346			−0.601721			−0.300860	−	0.953668i	$-0.597274\pi$
$719$	−16.1346			−0.601721			−0.300860	+	0.953668i	$0.597274\pi$
$720$	−1.70085	−	5.34203i	−0.0633870	−	0.199086i
$721$	15.6702			0.583588
$722$	15.4459	+	5.82108i	0.574838	+	0.216638i
$723$	−23.3295	−	23.3295i	−0.867632	−	0.867632i
$724$	−38.5225	−	33.8425i	−1.43168	−	1.25775i
$725$	3.05382	+	8.15884i	0.113416	+	0.303012i
$726$	3.74991	+	8.28579i	0.139172	+	0.307515i
$727$	13.4326	−	13.4326i	0.498186	−	0.498186i	−0.412687	−	0.910873i	$-0.635410\pi$
$727$	13.4326	−	13.4326i	0.498186	−	0.498186i	0.910873	+	0.412687i	$0.135410\pi$
$728$	−1.96020	+	1.04447i	−0.0726497	+	0.0387107i
$729$		−	30.0377i		−	1.11251i
$730$	19.5026	+	28.2595i	0.721822	+	1.04593i
$731$		−	20.1535i		−	0.745406i
$732$	1.97300	+	30.5074i	0.0729240	+	1.12759i
$733$	−9.61021	+	9.61021i	−0.354961	+	0.354961i	−0.861952	−	0.506990i	$-0.830758\pi$
$733$	−9.61021	+	9.61021i	−0.354961	+	0.354961i	0.506990	+	0.861952i	$0.330758\pi$
$734$	−37.5173	+	16.9792i	−1.38479	+	0.626716i
$735$	18.0692	+	12.5302i	0.666494	+	0.462185i
$736$	5.55851	−	3.43982i	0.204889	−	0.126793i
$737$	−11.0263	−	11.0263i	−0.406160	−	0.406160i
$738$	0.0839172	−	0.222670i	0.00308904	−	0.00819659i
$739$	48.4936			1.78387			0.891934	−	0.452166i	$-0.149349\pi$
$739$	48.4936			1.78387			0.891934	+	0.452166i	$0.149349\pi$
$740$	−5.14678	+	1.27948i	−0.189199	+	0.0470347i
$741$	−8.53172			−0.313421
$742$	−3.66177	+	9.71630i	−0.134428	+	0.356697i
$743$	12.7554	+	12.7554i	0.467951	+	0.467951i	0.901250	−	0.433299i	$-0.142651\pi$
$743$	12.7554	+	12.7554i	0.467951	+	0.467951i	−0.433299	+	0.901250i	$0.642651\pi$
$744$	5.83436	+	1.77812i	0.213898	+	0.0651892i
$745$	−4.42596	+	0.801169i	−0.162154	+	0.0293525i
$746$	1.69300	−	0.766203i	0.0619850	−	0.0280527i
$747$	1.42312	−	1.42312i	0.0520691	−	0.0520691i
$748$	19.4409	−	1.25729i	0.710828	−	0.0459711i
$749$			6.04491i			0.220876i
$750$	−13.9253	+	19.9846i	−0.508480	+	0.729736i
$751$			6.79567i			0.247977i	0.992284	+	0.123989i	$0.0395687\pi$
$751$			6.79567i			0.247977i	−0.992284	+	0.123989i	$0.960431\pi$
$752$	36.1036	+	27.8029i	1.31656	+	1.01387i
$753$	28.8938	−	28.8938i	1.05295	−	1.05295i
$754$	−1.01595	−	2.24483i	−0.0369985	−	0.0817518i
$755$	−14.8844	+	2.69431i	−0.541697	+	0.0980558i
$756$	−5.79144	+	6.59233i	−0.210633	+	0.239761i
$757$	−11.3555	−	11.3555i	−0.412722	−	0.412722i	0.469963	−	0.882686i	$-0.344267\pi$
$757$	−11.3555	−	11.3555i	−0.412722	−	0.412722i	−0.882686	+	0.469963i	$0.844267\pi$
$758$	0.316651	+	0.119336i	0.0115013	+	0.00433447i
$759$	4.65072			0.168810
$760$	−27.4840	+	21.7140i	−0.996951	+	0.787650i
$761$	31.0924			1.12710			0.563550	−	0.826082i	$-0.309435\pi$
$761$	31.0924			1.12710			0.563550	+	0.826082i	$0.309435\pi$
$762$	−31.8321	−	11.9965i	−1.15316	−	0.434589i
$763$	−7.23477	−	7.23477i	−0.261916	−	0.261916i
$764$	−7.81879	+	8.90004i	−0.282874	+	0.321992i
$765$	4.29418	+	2.97783i	0.155256	+	0.107664i
$766$	17.4905	+	38.6469i	0.631958	+	1.39637i
$767$	−8.61045	+	8.61045i	−0.310905	+	0.310905i
$768$	−21.3032	−	12.3981i	−0.768713	−	0.447379i
$769$			24.4534i			0.881812i	0.897553	+	0.440906i	$0.145343\pi$
$769$			24.4534i			0.881812i	−0.897553	+	0.440906i	$0.854657\pi$
$770$	−5.33955	+	3.68496i	−0.192424	+	0.132797i
$771$		−	15.7278i		−	0.566424i
$772$	10.8931	−	0.704483i	0.392050	−	0.0253549i
$773$	−17.9314	+	17.9314i	−0.644947	+	0.644947i	−0.951767	−	0.306820i	$-0.900735\pi$
$773$	−17.9314	+	17.9314i	−0.644947	+	0.644947i	0.306820	+	0.951767i	$0.400735\pi$
$774$	4.36523	−	1.97558i	0.156905	−	0.0710107i
$775$	2.45348	+	6.55491i	0.0881316	+	0.235459i
$776$	4.01516	−	13.1745i	0.144136	−	0.472937i
$777$	1.01442	+	1.01442i	0.0363921	+	0.0363921i
$778$	9.54217	−	25.3196i	0.342103	−	0.907753i
$779$	−1.48671			−0.0532669
$780$	3.55236	−	5.90294i	0.127195	−	0.211359i
$781$	−30.2194			−1.08134
$782$	−2.14873	+	5.70153i	−0.0768384	+	0.203886i
$783$	−6.88343	−	6.88343i	−0.245994	−	0.245994i
$784$	−25.3207	+	3.28886i	−0.904309	+	0.117459i
$785$	26.5345	−	38.2640i	0.947055	−	1.36570i
$786$	−44.1300	+	19.9720i	−1.57407	+	0.712378i
$787$	−31.8618	+	31.8618i	−1.13575	+	1.13575i	−0.146547	+	0.989204i	$0.546816\pi$
$787$	−31.8618	+	31.8618i	−1.13575	+	1.13575i	−0.989204	+	0.146547i	$0.953184\pi$
$788$	−0.946973	−	14.6426i	−0.0337345	−	0.521620i
$789$		−	35.5461i		−	1.26548i
$790$	−3.49819	+	19.0799i	−0.124460	+	0.678831i
$791$			8.75646i			0.311344i
$792$	2.17804	+	4.08761i	0.0773934	+	0.145247i
$793$	7.01616	−	7.01616i	0.249151	−	0.249151i
$794$	9.68621	+	21.4026i	0.343751	+	0.759550i
$795$	−5.73679	−	31.6922i	−0.203463	−	1.12401i
$796$	−9.33148	−	8.19782i	−0.330746	−	0.290564i
$797$	−13.3240	−	13.3240i	−0.471961	−	0.471961i	0.430588	−	0.902549i	$-0.358306\pi$
$797$	−13.3240	−	13.3240i	−0.471961	−	0.471961i	−0.902549	+	0.430588i	$0.858306\pi$
$798$	8.86618	+	3.34138i	0.313859	+	0.118284i
$799$	−42.4747			−1.50265
$800$	−3.57997	−	28.0568i	−0.126571	−	0.991958i
$801$	3.32161			0.117363
$802$	34.0223	+	12.8219i	1.20137	+	0.452759i
$803$	−20.0584	−	20.0584i	−0.707847	−	0.707847i
$804$	−13.8157	−	12.1373i	−0.487243	−	0.428049i
$805$	−0.361420	−	1.99662i	−0.0127384	−	0.0703717i
$806$	−0.816223	−	1.80352i	−0.0287502	−	0.0635264i
$807$	−1.62207	+	1.62207i	−0.0570994	+	0.0570994i
$808$	18.3122	+	34.3671i	0.644220	+	1.20903i
$809$			29.1355i			1.02435i	0.858881	+	0.512175i	$0.171160\pi$
$809$			29.1355i			1.02435i	−0.858881	+	0.512175i	$0.828840\pi$
$810$	3.83613	−	20.9230i	0.134788	−	0.735159i
$811$			28.0025i			0.983301i	0.870793	+	0.491650i	$0.163606\pi$
$811$			28.0025i			0.983301i	−0.870793	+	0.491650i	$0.836394\pi$
$812$	0.176603	+	2.73072i	0.00619753	+	0.0958293i
$813$	14.5081	−	14.5081i	0.508821	−	0.508821i
$814$	3.99172	−	1.80654i	0.139910	−	0.0633192i
$815$	−7.41132	+	10.6875i	−0.259607	+	0.374367i
$816$	22.7835	−	2.95932i	0.797584	−	0.103597i
$817$	−21.1679	−	21.1679i	−0.740573	−	0.740573i
$818$	−11.4989	+	30.5118i	−0.402051	+	1.06682i
$819$	0.492212			0.0171993
$820$	0.619022	−	1.02863i	0.0216172	−	0.0359212i
$821$	−41.7772			−1.45804			−0.729018	−	0.684495i	$-0.760023\pi$
$821$	−41.7772			−1.45804			−0.729018	+	0.684495i	$0.760023\pi$
$822$	4.49542	−	11.9283i	0.156796	−	0.416049i
$823$	19.6439	+	19.6439i	0.684742	+	0.684742i	0.961065	−	0.276323i	$-0.0891159\pi$
$823$	19.6439	+	19.6439i	0.684742	+	0.684742i	−0.276323	+	0.961065i	$0.589116\pi$
$824$	16.4542	−	53.9894i	0.573210	−	1.88081i
$825$	8.33843	−	18.3145i	0.290307	−	0.637631i
$826$	12.3202	−	5.57577i	0.428675	−	0.194006i
$827$	−3.98185	+	3.98185i	−0.138462	+	0.138462i	−0.772941	−	0.634478i	$-0.781215\pi$
$827$	−3.98185	+	3.98185i	−0.138462	+	0.138462i	0.634478	+	0.772941i	$0.281215\pi$
$828$	−1.44558	+	0.0934892i	−0.0502372	+	0.00324897i
$829$			7.84500i			0.272468i	0.990677	+	0.136234i	$0.0434999\pi$
$829$			7.84500i			0.272468i	−0.990677	+	0.136234i	$0.956500\pi$
$830$	8.35686	−	5.76727i	0.290071	−	0.200185i
$831$			9.50429i			0.329700i
$832$	1.54031	+	7.85032i	0.0534005	+	0.272161i
$833$	16.8291	−	16.8291i	0.583093	−	0.583093i
$834$	11.1543	+	24.6466i	0.386243	+	0.853441i
$835$	−4.27677	−	2.96576i	−0.148004	−	0.102634i
$836$	19.0988	−	21.7400i	0.660546	−	0.751893i
$837$	−5.53023	−	5.53023i	−0.191153	−	0.191153i
$838$	−20.1009	−	7.57539i	−0.694374	−	0.261688i
$839$	7.41725			0.256072			0.128036	−	0.991770i	$-0.459133\pi$
$839$	7.41725			0.256072			0.128036	+	0.991770i	$0.459133\pi$
$840$	−6.00346	+	4.74309i	−0.207139	+	0.163652i
$841$	25.9643			0.895321
$842$	3.67263	+	1.38410i	0.126567	+	0.0476992i
$843$	−20.9331	−	20.9331i	−0.720973	−	0.720973i
$844$	−17.4979	+	19.9177i	−0.602304	+	0.685596i
$845$	−2.20031	+	0.398291i	−0.0756930	+	0.0137016i
$846$	−4.16364	−	9.19996i	−0.143149	−	0.316301i
$847$	−2.31804	+	2.31804i	−0.0796489	+	0.0796489i
$848$	29.6312	+	22.8186i	1.01754	+	0.783593i
$849$			17.6106i			0.604393i
$850$	18.6001	+	18.6842i	0.637979	+	0.640862i
$851$			1.37035i			0.0469749i
$852$	−35.5642	+	2.30003i	−1.21841	+	0.0787977i
$853$	36.9719	−	36.9719i	1.26589	−	1.26589i	0.317705	−	0.948190i	$-0.397088\pi$
$853$	36.9719	−	36.9719i	1.26589	−	1.26589i	0.948190	−	0.317705i	$-0.102912\pi$
$854$	−10.0390	+	4.54338i	−0.343529	+	0.155471i
$855$	7.63805	−	1.38261i	0.261216	−	0.0472842i
$856$	20.8269	+	6.34737i	0.711849	+	0.216949i
$857$	13.5116	+	13.5116i	0.461548	+	0.461548i	0.899163	−	0.437614i	$-0.144177\pi$
$857$	13.5116	+	13.5116i	0.461548	+	0.461548i	−0.437614	+	0.899163i	$0.644177\pi$
$858$	−2.00723	+	5.32608i	−0.0685258	+	0.181830i
$859$	−11.1401			−0.380095			−0.190047	−	0.981775i	$-0.560864\pi$
$859$	−11.1401			−0.380095			−0.190047	+	0.981775i	$0.560864\pi$
$860$	23.4594	−	5.83199i	0.799960	−	0.198869i
$861$	−0.324748			−0.0110674
$862$	9.83907	−	26.1074i	0.335120	−	0.889223i
$863$	−12.6543	−	12.6543i	−0.430758	−	0.430758i	0.458128	−	0.888886i	$-0.348520\pi$
$863$	−12.6543	−	12.6543i	−0.430758	−	0.430758i	−0.888886	+	0.458128i	$0.848520\pi$
$864$	16.6317	+	26.8758i	0.565823	+	0.914332i
$865$	−38.0133	−	26.3606i	−1.29249	−	0.896288i
$866$	25.0703	−	11.3461i	0.851922	−	0.385556i
$867$	3.37549	−	3.37549i	0.114638	−	0.114638i
$868$	0.141885	+	2.19389i	0.00481588	+	0.0744655i
$869$		−	16.0258i		−	0.543638i
$870$	−4.82104	−	6.98575i	−0.163449	−	0.236839i
$871$			5.96873i			0.202243i
$872$	−32.5232	+	17.3296i	−1.10137	+	0.586856i
$873$	−2.15819	+	2.15819i	−0.0730437	+	0.0730437i
$874$	3.73163	+	8.24540i	0.126224	+	0.278905i
$875$	−8.51070	−	2.15654i	−0.287714	−	0.0729042i
$876$	−25.1327	−	22.0794i	−0.849156	−	0.745993i
$877$	19.6944	+	19.6944i	0.665033	+	0.665033i	0.956562	−	0.291529i	$-0.0941639\pi$
$877$	19.6944	+	19.6944i	0.665033	+	0.665033i	−0.291529	+	0.956562i	$0.594164\pi$
$878$	28.1615	+	10.6132i	0.950403	+	0.358177i
$879$	37.6800			1.27092
$880$	7.08929	+	22.2660i	0.238980	+	0.750587i
$881$	−36.9053			−1.24337			−0.621686	−	0.783266i	$-0.713552\pi$
$881$	−36.9053			−1.24337			−0.621686	+	0.783266i	$0.713552\pi$
$882$	5.29484	+	1.99546i	0.178287	+	0.0671906i
$883$	31.2868	+	31.2868i	1.05288	+	1.05288i	0.998521	+	0.0543625i	$0.0173126\pi$
$883$	31.2868	+	31.2868i	1.05288	+	1.05288i	0.0543625	+	0.998521i	$0.482687\pi$
$884$	−5.60211	−	4.92152i	−0.188419	−	0.165529i
$885$	−23.9030	+	34.4693i	−0.803490	+	1.15867i
$886$	4.38963	+	9.69930i	0.147472	+	0.325854i
$887$	39.5773	−	39.5773i	1.32888	−	1.32888i	0.422524	−	0.906352i	$-0.361144\pi$
$887$	39.5773	−	39.5773i	1.32888	−	1.32888i	0.906352	−	0.422524i	$-0.138856\pi$
$888$	4.56022	−	2.42987i	0.153031	−	0.0815409i
$889$		−	12.2616i		−	0.411240i
$890$	16.4832	+	3.02210i	0.552517	+	0.101301i
$891$			17.5739i			0.588748i
$892$	0.924322	+	14.2923i	0.0309486	+	0.478542i
$893$	−44.6126	+	44.6126i	−1.49291	+	1.49291i
$894$	3.99249	−	1.80689i	0.133529	−	0.0604314i
$895$	−7.64095	−	42.2115i	−0.255409	−	1.41097i
$896$	1.47383	−	8.76131i	0.0492371	−	0.292695i
$897$	−1.25875	−	1.25875i	−0.0420285	−	0.0420285i
$898$	−3.95203	+	10.4865i	−0.131881	+	0.349939i
$899$	−2.43892			−0.0813424
$900$	−2.22366	+	5.86030i	−0.0741220	+	0.195343i
$901$	−34.8601			−1.16136
$902$	−0.349773	+	0.928105i	−0.0116462	+	0.0309025i
$903$	−4.62381	−	4.62381i	−0.153871	−	0.153871i
$904$	30.1692	+	9.19458i	1.00341	+	0.305807i
$905$	10.2115	+	56.4123i	0.339443	+	1.87521i
$906$	13.4266	−	6.07651i	0.446070	−	0.201879i
$907$	−27.4733	+	27.4733i	−0.912236	+	0.912236i	−0.996448	−	0.0842123i	$-0.973163\pi$
$907$	−27.4733	+	27.4733i	−0.912236	+	0.912236i	0.0842123	+	0.996448i	$0.473163\pi$
$908$	48.5302	−	3.13858i	1.61053	−	0.104157i
$909$		−	8.62970i		−	0.286229i
$910$	2.44255	+	0.447829i	0.0809698	+	0.0148454i
$911$		−	18.0519i		−	0.598087i	−0.954239	−	0.299044i	$-0.903332\pi$
$911$		−	18.0519i		−	0.598087i	0.954239	−	0.299044i	$-0.0966676\pi$
$912$	20.8221	−	27.0386i	0.689487	−	0.895338i
$913$	−5.93165	+	5.93165i	−0.196309	+	0.196309i
$914$	23.9454	+	52.9095i	0.792042	+	1.75009i
$915$	19.4772	−	28.0871i	0.643896	−	0.928530i
$916$	19.7518	−	22.4833i	0.652619	−	0.742869i
$917$	−12.3459	−	12.3459i	−0.407697	−	0.407697i
$918$	−27.5673	−	10.3892i	−0.909856	−	0.342896i
$919$	6.59248			0.217466			0.108733	−	0.994071i	$-0.465321\pi$
$919$	6.59248			0.217466			0.108733	+	0.994071i	$0.465321\pi$
$920$	−7.25858	−	0.851298i	−0.239308	−	0.0280665i
$921$	30.0360			0.989720
$922$	−2.74263	−	1.03361i	−0.0903238	−	0.0340402i
$923$	8.17913	+	8.17913i	0.269219	+	0.269219i
$924$	4.17184	−	4.74876i	0.137243	−	0.156223i
$925$	5.39643	+	2.45694i	0.177433	+	0.0807837i
$926$	−3.27726	−	7.24141i	−0.107697	−	0.237967i
$927$	−8.84431	+	8.84431i	−0.290485	+	0.290485i
$928$	9.59374	+	2.25889i	0.314930	+	0.0741516i
$929$			22.3759i			0.734128i	0.930196	+	0.367064i	$0.119637\pi$
$929$			22.3759i			0.734128i	−0.930196	+	0.367064i	$0.880363\pi$
$930$	−3.87328	−	5.61244i	−0.127010	−	0.184039i
$931$		−	35.3523i		−	1.15862i
$932$	−34.5493	+	2.23440i	−1.13170	+	0.0731901i
$933$	21.7062	−	21.7062i	0.710630	−	0.710630i
$934$	−3.29279	+	1.49022i	−0.107743	+	0.0487616i
$935$	−17.8985	−	12.4118i	−0.585343	−	0.405910i
$936$	0.516840	−	1.69585i	0.0168934	−	0.0554305i
$937$	−4.23718	−	4.23718i	−0.138423	−	0.138423i	0.634500	−	0.772923i	$-0.281206\pi$
$937$	−4.23718	−	4.23718i	−0.138423	−	0.138423i	−0.772923	+	0.634500i	$0.781206\pi$
$938$	2.33761	−	6.20271i	0.0763255	−	0.202526i
$939$	24.6081			0.803054
$940$	−12.2912	−	49.4421i	−0.400896	−	1.61262i
$941$	−0.767836			−0.0250307			−0.0125154	−	0.999922i	$-0.503984\pi$
$941$	−0.767836			−0.0250307			−0.0125154	+	0.999922i	$0.503984\pi$
$942$	−15.9992	+	42.4531i	−0.521283	+	1.38320i
$943$	−0.219346	−	0.219346i	−0.00714289	−	0.00714289i
$944$	−6.27391	−	48.3023i	−0.204199	−	1.57211i
$945$	9.65380	−	1.74749i	0.314038	−	0.0568459i
$946$	−18.1946	+	8.23436i	−0.591557	+	0.267722i
$947$	−13.0954	+	13.0954i	−0.425544	+	0.425544i	−0.887107	−	0.461563i	$-0.847289\pi$
$947$	−13.0954	+	13.0954i	−0.425544	+	0.425544i	0.461563	+	0.887107i	$0.347289\pi$
$948$	−1.21974	−	18.8602i	−0.0396152	−	0.612550i
$949$			10.8579i			0.352464i
$950$	39.1610	+	0.0882722i	1.27055	+	0.00286393i
$951$			6.21631i			0.201578i
$952$	3.89425	+	7.30848i	0.126213	+	0.236869i
$953$	9.99529	−	9.99529i	0.323779	−	0.323779i	−0.526436	−	0.850215i	$-0.676472\pi$
$953$	9.99529	−	9.99529i	0.323779	−	0.323779i	0.850215	+	0.526436i	$0.176472\pi$
$954$	−3.41721	−	7.55064i	−0.110636	−	0.244461i
$955$	13.0332	−	2.35922i	0.421745	−	0.0763425i
$956$	−1.83955	−	1.61606i	−0.0594952	−	0.0522672i
$957$	4.95845	+	4.95845i	0.160284	+	0.160284i
$958$	−35.1845	−	13.2599i	−1.13676	−	0.428409i
$959$	4.59473			0.148372
$960$	10.0378	+	25.6645i	0.323969	+	0.828318i
$961$	29.0405			0.936792
$962$	−1.56934	−	0.591436i	−0.0505977	−	0.0190687i
$963$	−3.41177	−	3.41177i	−0.109943	−	0.109943i
$964$	−32.1794	−	28.2699i	−1.03643	−	0.910513i
$965$	−10.0288	−	6.95457i	−0.322840	−	0.223876i
$966$	0.815117	+	1.80108i	0.0262260	+	0.0579488i
$967$	3.66071	−	3.66071i	0.117721	−	0.117721i	−0.645792	−	0.763513i	$-0.723473\pi$
$967$	3.66071	−	3.66071i	0.117721	−	0.117721i	0.763513	+	0.645792i	$0.223473\pi$
$968$	5.55247	+	10.4205i	0.178463	+	0.334928i
$969$			31.8100i			1.02188i
$970$	−12.6734	+	8.74622i	−0.406918	+	0.280824i
$971$		−	46.0527i		−	1.47790i	−0.673760	−	0.738950i	$-0.735322\pi$
$971$		−	46.0527i		−	1.47790i	0.673760	−	0.738950i	$-0.264678\pi$
$972$	−0.825931	−	12.7710i	−0.0264918	−	0.409629i
$973$	−6.89515	+	6.89515i	−0.221048	+	0.221048i
$974$	12.1276	−	5.48859i	0.388592	−	0.175866i
$975$	−7.21383	+	2.70011i	−0.231028	+	0.0864728i
$976$	5.11225	+	39.3588i	0.163639	+	1.25984i
$977$	−3.29360	−	3.29360i	−0.105372	−	0.105372i	0.652455	−	0.757827i	$-0.273739\pi$
$977$	−3.29360	−	3.29360i	−0.105372	−	0.105372i	−0.757827	+	0.652455i	$0.773739\pi$
$978$	4.46873	−	11.8575i	0.142894	−	0.379162i
$979$	−13.8447			−0.442480
$980$	24.4596	+	14.7197i	0.781333	+	0.470203i
$981$	8.16667			0.260742
$982$	−5.11744	+	13.5788i	−0.163304	+	0.433318i
$983$	−5.64062	−	5.64062i	−0.179908	−	0.179908i	0.611408	−	0.791316i	$-0.290604\pi$
$983$	−5.64062	−	5.64062i	−0.179908	−	0.179908i	−0.791316	+	0.611408i	$0.790604\pi$
$984$	−0.340997	+	1.11887i	−0.0108706	+	0.0356684i
$985$	−9.34841	+	13.4809i	−0.297865	+	0.429537i
$986$	−8.36970	+	3.78789i	−0.266546	+	0.120631i
$987$	−9.74494	+	9.74494i	−0.310185	+	0.310185i
$988$	−11.0533	+	0.714848i	−0.351653	+	0.0227423i
$989$		−	6.24615i		−	0.198616i
$990$	0.933862	−	5.09347i	0.0296801	−	0.161881i
$991$			18.3567i			0.583120i	0.956553	+	0.291560i	$0.0941742\pi$
$991$			18.3567i			0.583120i	−0.956553	+	0.291560i	$0.905826\pi$
$992$	7.70772	+	1.81482i	0.244721	+	0.0576205i
$993$	11.3442	−	11.3442i	0.359996	−	0.359996i
$994$	−5.29647	−	11.7031i	−0.167994	−	0.371198i
$995$	2.47358	+	13.6650i	0.0784179	+	0.433210i
$996$	−6.52929	+	7.43221i	−0.206888	+	0.235499i
$997$	−1.94369	−	1.94369i	−0.0615574	−	0.0615574i	0.675658	−	0.737215i	$-0.263860\pi$
$997$	−1.94369	−	1.94369i	−0.0615574	−	0.0615574i	−0.737215	+	0.675658i	$0.763860\pi$
$998$	−30.0513	−	11.3254i	−0.951256	−	0.358498i
$999$	−6.62572			−0.209628

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.o.a.27.34	yes	72
4.3	odd	2	inner	260.2.o.a.27.22	✓	72
5.3	odd	4	inner	260.2.o.a.183.22	yes	72
20.3	even	4	inner	260.2.o.a.183.34	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.o.a.27.22	✓	72	4.3	odd	2	inner
260.2.o.a.27.34	yes	72	1.1	even	1	trivial
260.2.o.a.183.22	yes	72	5.3	odd	4	inner
260.2.o.a.183.34	yes	72	20.3	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.32335 + 0.498731i) q^{2} +(1.08931 + 1.08931i) q^{3} +(1.50254 + 1.32000i) q^{4} +(-0.398291 - 2.20031i) q^{5} +(0.898273 + 1.98482i) q^{6} +(-0.555275 + 0.555275i) q^{7} +(1.33007 + 2.49618i) q^{8} -0.626800i q^{9} +O(q^{10})\)	\(q+(1.32335 + 0.498731i) q^{2} +(1.08931 + 1.08931i) q^{3} +(1.50254 + 1.32000i) q^{4} +(-0.398291 - 2.20031i) q^{5} +(0.898273 + 1.98482i) q^{6} +(-0.555275 + 0.555275i) q^{7} +(1.33007 + 2.49618i) q^{8} -0.626800i q^{9} +(0.570281 - 3.11043i) q^{10} +2.61255i q^{11} +(0.198844 + 3.07462i) q^{12} +(0.707107 - 0.707107i) q^{13} +(-1.01176 + 0.457894i) q^{14} +(1.96296 - 2.83069i) q^{15} +(0.515226 + 3.96668i) q^{16} +(-2.63640 - 2.63640i) q^{17} +(0.312604 - 0.829478i) q^{18} -5.53821 q^{19} +(2.30595 - 3.83179i) q^{20} -1.20974 q^{21} +(-1.30296 + 3.45733i) q^{22} +(-0.817097 - 0.817097i) q^{23} +(-1.27026 + 4.16798i) q^{24} +(-4.68273 + 1.75273i) q^{25} +(1.28841 - 0.583097i) q^{26} +(3.95072 - 3.95072i) q^{27} +(-1.56728 + 0.101360i) q^{28} -1.74233i q^{29} +(4.00944 - 2.76701i) q^{30} -1.39981i q^{31} +(-1.29648 + 5.50628i) q^{32} +(-2.84588 + 2.84588i) q^{33} +(-2.17404 - 4.80375i) q^{34} +(1.44294 + 1.00062i) q^{35} +(0.827373 - 0.941789i) q^{36} +(-0.838546 - 0.838546i) q^{37} +(-7.32902 - 2.76208i) q^{38} +1.54052 q^{39} +(4.96262 - 3.92076i) q^{40} +0.268446 q^{41} +(-1.60091 - 0.603332i) q^{42} +(3.82216 + 3.82216i) q^{43} +(-3.44855 + 3.92545i) q^{44} +(-1.37915 + 0.249649i) q^{45} +(-0.673798 - 1.48882i) q^{46} +(8.05542 - 8.05542i) q^{47} +(-3.75971 + 4.88219i) q^{48} +6.38334i q^{49} +(-7.07105 - 0.0159388i) q^{50} -5.74373i q^{51} +(1.99583 - 0.129076i) q^{52} +(6.61129 - 6.61129i) q^{53} +(7.19854 - 3.25786i) q^{54} +(5.74842 - 1.04056i) q^{55} +(-2.12462 - 0.647516i) q^{56} +(-6.03284 - 6.03284i) q^{57} +(0.868951 - 2.30571i) q^{58} -12.1770 q^{59} +(6.68591 - 1.66211i) q^{60} +9.92235 q^{61} +(0.698126 - 1.85244i) q^{62} +(0.348046 + 0.348046i) q^{63} +(-4.46185 + 6.64017i) q^{64} +(-1.83749 - 1.27422i) q^{65} +(-5.18544 + 2.34678i) q^{66} +(-4.22053 + 4.22053i) q^{67} +(-0.481251 - 7.44133i) q^{68} -1.78015i q^{69} +(1.41048 + 2.04381i) q^{70} +11.5670i q^{71} +(1.56461 - 0.833685i) q^{72} +(-7.67772 + 7.67772i) q^{73} +(-0.691485 - 1.52790i) q^{74} +(-7.01022 - 3.19168i) q^{75} +(-8.32136 - 7.31041i) q^{76} +(-1.45068 - 1.45068i) q^{77} +(2.03865 + 0.768304i) q^{78} -6.13415 q^{79} +(8.52271 - 2.71355i) q^{80} +6.72672 q^{81} +(0.355249 + 0.133882i) q^{82} +(2.27045 + 2.27045i) q^{83} +(-1.81767 - 1.59685i) q^{84} +(-4.75085 + 6.85096i) q^{85} +(3.15185 + 6.96431i) q^{86} +(1.89794 - 1.89794i) q^{87} +(-6.52140 + 3.47486i) q^{88} +5.29932i q^{89} +(-1.94962 - 0.357452i) q^{90} +0.785278i q^{91} +(-0.149153 - 2.30628i) q^{92} +(1.52482 - 1.52482i) q^{93} +(14.6777 - 6.64270i) q^{94} +(2.20582 + 12.1858i) q^{95} +(-7.41033 + 4.58579i) q^{96} +(-3.44319 - 3.44319i) q^{97} +(-3.18357 + 8.44742i) q^{98} +1.63755 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) \) 72 * q - 8 * q^6 - 12 * q^8	\( 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) \) 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

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